Irish Hermit,
Carthage 411 upheld the Augustinian view on baptism by heretics and this came to hold sway in the Western Church. The Orthodox hold to the earlier views of another Carthage man, Saint Cyprian, who developed an uncompromising theology of "extra ecclesiam nulla sacramenta" - no sacraments outside the Church. With exceptions for the exercise of economia in the reception of some heretics this is still the base teaching of the Orthodox today.
This topic is not nearly as simple as you're representing it. To state that St.Cyprian's view is
the "Orthodox view" is also not factual. The reality is, when all is said and done, that there is not a single Orthodox intepretation of just what does/does not happen when heterodox/schismatic bodies administer baptisms under a proper form.
What is known, and can be stated without doubt, is that the Orthodox Church is the Church of Christ. It is in that continuity, She administers valid Sacraments. When people fall from this fullness of truth, or when they splinter from this visible unity, just what it is they are doing is ultimatly known by God. To say absolutely and in every case that there "is no grace" is a presumption, and one which sometimes is demonstrated to be wrong by historical fact - for example, when through misunderstanding and political circumstance, two parties which later history will recognize as both being Orthodox have been separated from one another, even to the point of enmity (this happened many times during the Arian and other early Christological controversies.) Of course, those are things determined by hindsight.
Both the Augustinian and Cyprianic opinions are interpretations of available information - they are educated, and important opinions on what happens when canonical boundaries are broken. The Cyprianic view takes canonical boundaries at face value, and says when you trespass this, all bets are off. This makes sense to an extent, but history shows it is not an infallible measure either (that the canons can always accurately describe reality). It also goes without saying that St.Cyprians views about how non-Orthodox Christians
need to be received into the Church (by Baptism only) has
never been considered an absolute norm - in fact, the contrary is true. As for the Augustinian opinion, while it is more penetrating and takes a larger number of things into consideration, it fails to be 100% comprehensive for other reasons - like for example, what about schisms based totally on malice & stupidity; if as St.Augustine teaches, sacraments administered in suct sects are valid but not fruitful, why on earth would they be valid at all? The objection of Metropolitan Anthony Khrapovitsky earlier in the 20th century makes perfect sense here - is there such a thing as "half grace" - why would God grant that the bread and wine would transform into His Body and Blood, only to be taken sacreligiously by malicious sectarians?
My understanding is the canons deal with what can be known. Thus why, generally, most Orthodox
do accept the opinion of the compiler of canons, St.Nikodemos the Hagiorite, that the Church can and does accept certain types of heretics and schismatics without "repeating" certain sacraments, because if something is lacking, She can "fill" that in by receiving them. OTOH, the Church can also "repeat" sacraments so administered, if necessary, precisely because the circumstances allow that wherever there is doubt, this can happen for the sake of peace. For example, if there is real doubt that someone raised Orthodox was in fact baptized properly (lack of certificates, witnesses, etc.), he can be Baptized - even if it's also quite possible this would be a "second baptism".
Generally, unless there is some serious doubt that the form was administered properly, most Orthodox Bishops outside of Greece or Jerusalem (this includes Bishops of many ethnicities and immediate loyalties, not simply Slavs) will not receive Roman Catholics and most confessional Protestants via Baptism. Though the practice differs (and the Americas there seems to be some confusion on the matter - though in Europe this is less often the case), generally Roman/Uniate Catholics, Non-Chalcedonians, etc. will be received via repentence, confession, and profession of faith - and certain Protestants (generally of the continental/confessional variety that maintain the practice of threefold baptism, even if it is by pouring) by Chrismation.
Receiving converts from Roman Catholicism by Baptism is a complicated matter. A lot of it hinges not so much upon the fact they're separated from the canonical unity of the Church, but upon the form; pouring. The Greek answer to this
was generally that it did not count - in Greece, Mt.Athos, and the Greek Orthodox Patriarchate of Jerusalem, this is generally how it's remained. The EP did take this posture, but has reconsidered it in recent decades. I'm inclined to think the argument in favour of this practice is poor. In effect, the Greek Churches that keep this practice do not accept the old reasoning for it - since they remain in communion with the rest of the Orthodox world which do not insist that Churches
need to receive all heterodox and schismatics
only by Baptism.
The Russians went back and forth on this for a little while, after it became common for Latins to baptize only by pouring (which you have to remember is a relatively recent thing - before that they used threefold immersion, and when this was the case, none of this was an issue). However for centuries now, it's been a very firm matter of discipline, that Roman Catholics are only received via confession (or if they haven't been Confirmed, via Chrismation.)
The only time Latin converts are received via Baptism outside of the exceptions I mentioned, is either by clergy who have problems with obedience (they think they know better than their Bishops or Synod),
or to assuage the consciences of very scupelous converts - or in some cases, when there are doubts that the convert from Catholicism was in fact given the proper form of baptism (ex. baptismal papers cannot be produced.)
