"Is this believable?" -I think so.
"How is this, they're present invisibly but they're not present at all?" -Read below.
"Isn't it better to say that the 'institution narrative' is not, after all, the condition si ne qua non of having a valid consecration?" -Not from the Latin Church's point of view. Considering that every extent Anaphora, East and West except those of Mar Addai and Mar Mari of the Assyrians/Chaldeans and that of Peter III of the Syriacs/Maronites, includes the Institution Narrative and the importance of the Institution Narrative in those traditions especially the Latin, even while recognizing the East believes the Consecration isn't complete until the Epiclesis the Latin Church needed this explanation.
Fr. Deacon Lance
"Finally, it must be observed that the eastern and western Eucharistic Anaphoras, while expressing the same mystery, have different theological, ritual and linguistic traditions. The words of the Eucharistic Institution are indeed present in the Anaphora of Addai and Mari, not in a coherent way and ad litteram, but rather in a dispersed euchological way, that is, integrated in prayers of thanksgiving, praise and intercession. All these elements constitute a “quasi-narrative” of the Eucharistic Institution. In the central part of the Anaphora, together with the Epiclesis, explicit references are made to the eucharistic Body and Blood of Jesus Christ
(“O my Lord, in thy manifold and ineffable mercies, make a good and gracious remembrance for all the upright and just fathers who were pleasing before thee, in the commemoration of the body and blood of thy Christ, which we offer to thee upon the pure and holy altar, as thou hast taught us”)
to the life-giving mystery of Jesus’ passion, death and resurrection, which is actually commemorated and celebrated
(“that all the inhabitants of the world may know thee ... and we also, O my Lord, thy unworthy, frail and miserable servants who are gathered and stand before thee, and have received by tradition the example which is from thee, rejoicing and glorifying and exalting and commemorating and celebrating this great and awesome mystery of the passion and death and resurrection of our Lord Jesus Christ”),
to the eucharistic offering for the forgiveness of the sins, to the eschatological dimension of the eucharistic celebration and to the Lord’s command to 'do this in memory of me'
(“And let thy Holy Spirit come, O my Lord, and rest upon this offering of thy servants, and bless it and sanctify it that it my be to us, O my Lord, for the pardon of sins, and for the forgiveness of shortcomings, and for the great hope of the resurrection from the dead, and for new life in the kingdom of heaven with all who have been pleasing before thee”).
So the words of the Institution are not absent in the Anaphora of Addai and Mari, but explicitly mentioned in a dispersed way, from the beginning to the end, in the most important passages of the Anaphora. It is also clear that the passages cited above express the full conviction of commemorating the Lord’s paschal mystery, in the strong sense of making it present; that is, the intention to carry out in practice precisely what Christ established by his words and actions in instituting the Eucharist." http://www.vatican.va/roman_curia/pontifical_councils/chrstuni/documents/rc_pc_chrstuni_doc_20011025_chiesa-caldea-assira_en.html