In all these letters both the emperor and Photius emphatically acknowledge the Roman primacy and categorically invoke the pope's jurisdiction to confirm what has happened.
What we have here is a microcosm of Catholic apologetics and the way that Orthodox can many times respond to the apologetic. If you examine this situation, you can take what you learn and apply it to almost all the other quotes and arguments which seem
to support Roman primacy. In this case, St. Photius and the Emperor did indeed speak of Rome (and to Rome) in very complimentary terms at times. This was the standard rhetorical procedure of the day: people were just overly-flowery and polite and complimentary (sometimes to a fault). Thus at first, when the Pope of Rome reacted very badly to his consecration, St. Photius tried (in Letter 1) to sweet talk him with a lot of stuff about love, how he hadn't really wanted to be Patriarch, etc. What he also says, however, even in this early stage is that Constantinople rules Constantinople, not Rome. When Photius was first elevated, Rome reacted very badly and refused to acknowledge St. Photius. Besides speaking of love and other such matters, St. Photius responds to the Pope with these words:
You say that the canons were violated when I, a layman, came so quickly to the bishopric. But, we ask, which canon have we violated? For up until now, the Church of Constantinople has never accepted any such canon. Therefore, a rule that does not exist cannot be broken. If, because of this, I should be dethroned, then our holy and blessed Fathers and Patriarchs Nicephoros and Tarasios would have been in danger of being removed, for they were chosen for the hierarchy while laymen, benig the brightest luminaries of our generation and brilliant confessors of the Truth Fath and of piety, and in their lives and words the Truth was maintained... Even among the Latins there have been hierarchs who, although layman, were elevated to the rank of bishops, for example, St. Ambrose, the adornment of all Latins. So also St. Nectarios, whose episcopal election was confirmed by a full Ecumenical Council while he was still a layman... After all, I must say, obedience to rules cannot be required of those to whom the rules are not given. - Letter 1, 2
The last sentence seems important to me: St. Photius clearly implies that in his and his Church's understanding, Rome cannot simply say something and it become law. Rome's might have primacy of honor, but for their word to have any meaning it must be accepted by another Church. Photius says that "the Church of Constantinople has never accepted any such canon" (ie. a canon prohibiting the elevation of lay people quickly to bishop), and "the pope says so" didn't hold any weight for him (or other bishops). St. Photius continues:
That which is common to all must necessarily be preserved in its entirety; most of all, in that which concerns the Faith, the least departure from which is a grave sin. All that is prescribed by common ecumenical decision must be held by all. But if one of the Fathers prescribes something for himself, or if something is ordained by some local council, then that must be held by those who have accepted it, and it is not a grave matter if it is not held by those who have not received it.- Letter 1,2
The context of this letter is that the Pope was essentially trying to put his foot down. His basic position was "A Local Council says it, Rome says it, case closed". But Photius clearly shows that for himself (and indeed for all of Orthodoxy), it just doesn't work that way. The only thing that someone is required to hold is what everyone has agreed to hold to, through an Ecumenical Council or at least through Church-wide acceptance. Yet, St. Photius wanted peace to prevail, so he agreed to address the Pope's issue in such a way that it wouldn't happen again, not because the Pope's word was law, but out of love:
Concerning the elevation of a layman to the rank of hierarch, let it be known that this is entirely in accord with the holy Fathers. Not only do their words confirm this, but their very deeds and actions which at various times have served for the great benefit of the Bride of Christ--the Church. All that we have said and cited has not been for the sake of bickering, but rather to show the true state of the matter. If this has offended anyone, then one can, out of love for his brother, change that which, when corrected, will cause no harm. So, from this time, by conciliar decree, the custom will be established among us that no on from among the laity will be immediately elevated to the rank of bishop.
What is really interesting is that, not only does St. Photius act based on love and not Roman will, but earlier in the letter he also lists problems that he is aware of in the Roman Church; thus this paragraph implies that Rome should do some cleaning up of it's own Church to help avoid scandal! After listing some of the differences, St. Photius says:
Even so, I must say that some of the customs we have observed among you are not without fault, or above reproach, since some of them can be considered incorrect and, therefore, must be rejected... who can dare to despise and scorn the dogmas of the Lord, the Fathers, and the Councils?
St. Photius even goes so far as to advise the Pope how to proceed in the future when situations occur similar to the one that had caused the problem they were in:
It is necessary that in all things you hold fast to correct and true canons of the Church and to the order of the Church... Your Beatitude must put a stop to this... - Letter 1, 2
It is true that the Church of Rome did eventually persuade people in Constantinople to condemn Photius, and this Council has remained an Ecumenical one for Roman Catholics. However, about ten years later the Orthodox held another Council which vindicated St. Photius, and he eventually even became Patriarch again. Some Orthodox consider this Photian Council Ecumenical, though even if it is not it is considered to have binding authority. In spite of Constantinople's reversal of the Roman-led Council, and their reinstallation of Photius, Rome did not have a problem entering back into communion with Constantinople--on and off at least--for another 150 or 200 years. Orthodoxy had essentially said no to Rome's claim to universal primacy, and Rome remained in communion with her.
Now, after all this, am I claiming that the Emperor and Patirarchs never acknowledged Roman primacy? No. Unfortunately, sometimes Orthodox writers did
go too far, and we suffer the consequences till this day. What I would say, though, is that you cannot take ornate or complimentary language and try to pretend that they are precise theological statements that prove Roman primacy. According to St. Photius' own words, you cannot simply take what one many or Local Council says and force the rest of the Church to abide by those words. If the Emperor or anyone else made a theological mistake (ie. affirming some primacy that Rome didn't really have), then it remains a mistake to be avoided, not a belief that must be followed due to the authority of the one making the mistake.
And when you examine real life
applications of theological principles, it is quite clear that neither the Emperors nor Patriarchs of Constantinople considered Rome as having some type of overarching primacy. The missionizing of Bulgaria is a great example, as both Rome and Constantinople fought hard over this land's conversion, and there is not even a hint of submission to Rome in this matter, in spite of it being a matter of the faith.