Here is what the Creed says:
"Τόν διÂ’ ημάς τούς ανθρώπους καί διά τήν ημετέραν σωτηρίαν κατελθόντα εκ τών ουρανών καί σαρκωθέντα εκ Πνεύματος ‘Αγίου καί Μαρίας τής Παρθένου καί ενανθρωπήσαντα."
Notice how The Fathers framed this statement of the Incarnation by attributing the "σαρκωθέντα" (enfleshment is probaby the best way to put it but there really is more to it than that) to the Holy Spirit and Mary the Virgin and then saying "ενανθρωπήσαντα", roughly was made or became human. What the Fathers are describing is a completely unique event in human history. The other theophanies you refer to are God taking a form of something human, but not "σαρκωθέντα" or "ενανθρωπήσαντα". To argue otherwise is to deny the uniqueness of the Incarnation.
So yes, as explained above, I support Kosta's statement.
Maybe this will help. Creeds aside, the word in inspired Scripture is Ginomai (egeneto).
Outline of Biblical Usage
1) to become, i.e. to come into existence, begin to be, receive being
2) to become, i.e. to come to pass, happen
a) of events
3) to arise, appear in history, come upon the stage
a) of men appearing in public
4) to be made, finished
a) of miracles, to be performed, wrought
5) to become, be made