A first problem is that there is in GR no such thing as "an observers frame", except in sloppy speech. There are various systems of coordinates. Two systems of coordinates may agree for an observer as much as one likes but differ elsewhere. And all the systems of coordinates are on equal foot, none is preferred.
What could replace the "observer's frame"? The most plausible candidate seems to be the use of harmonic coordinates - they really essentially simplify the <PERSON> equations, are used in the Newtonian limit and in the PPN formalism (see here) or in <PERSON> local existence and uniqueness proof, roughly the only reasonable candidate for preferred coordinates. To define harmonic coordinates, one need some initial values, because the harmonic condition is only an evolution equation $\square X^\mu = 0$ for them, but this is given by the <PERSON> coordinates before the collapse. 578
This gives, roughly, the Schwarzschild time coordinate, thus, it would be such a system of coordinates where the material of the collapsing star never reaches the horizon.
From point of view of classical GR, the only objection is that these coordinates would not cover the complete solution.
If one includes Hawking radiation into the consideration, one should care about the trans-Planckian problem (to derive that Hawking radiation lasts more than a second after the collapse, one has to presuppose that semiclassical theory remains valid for distances of $10^{-1000}$ of Planck length or so). The mainstream way to solve this problem is to rely on some results of <PERSON> and others that some Hawking radiation remains if one considers various regularizations. The problem is that these regularizations break covariance, thus, require preferred coordinates, and they obtain <PERSON> radiation only if the preferred coordinates are those related with the infalling observers. If they are stationary, there will be no <PERSON> radiation. And if one wants to rely on modifications of GR with preferred coordinates, see above for candidates.
If one ignores this and assumes Hawking radiation, then one can publish the idea that the BH evaporates before being formed even in Phys.Rev., as done by <PERSON>, PRD 14, 1479 (1976), and get citations by standard textbooks like <PERSON>, <PERSON>, quantum fields in curved spacetime, so it is close enough to being tenable. 469