Offensive foul / basket counts?

[ram]

V1 driving to basket. H1 has position in his path. V1 shoots, whistle sounds. Official on baseline (O1) calls offensive foul on V1 and gives the signal.
Ball goes in, O1 waves off shot. O2 (at half court) says shot should count. The confer for a moment and decide the basket counts.

Yes, I am the coach of H. This was in the last minute of OT and was the last basket made, we lost.

Confused on how an offensive foul results in basket counting? From my understanding, once the shot leaves the fingers, there is no possession, thus no "offensive" foul.

If it was an offensive foul, then how can the basket count?

From my recollection the sequence was:
Shot, whistle, ball goes in.


Thanks in advance.