I mean, if you want to stonewall that, sure he cannot legitimately prove she's Ayaya from that. But you are moving the goalpost from him believing or thinking that Shirayuki is Ayaya to having it confirmed by her.
Which, again, will mean you need to wait until next chapter.
I... just want to clarify that, what I have tried to get at all these time is, without FMC fumbling, no one can proves her to be Ayaya, no matter how strong the case they can build, and I don't deny that the case we have here, MC & Yellowman won't believe its not her. We'll just get a little more of proving her identity go on a little longer with MC being all suspicious. But, because she had fumbled as you pointed out, she just can't deny it anymore.
It's a hypothetical situation that's really meaningless, yeah. Just trying to propose that if she had not fumbled, she could have get away with it for a little longer -- probably very little, but still a bit longer than this. Is that a good development? From the pacing so far, probably not, but that would be a way that many romcom from previous era would go to milk some more chapters out of this situation. And probably because I've seen characters in this series showing to be more sensible that typical romcom will go with, I'm a little disappoint it ends with just she fumbling herself, I guess. Probably more concrete way to end this shenanigan might be more satisfy to me.
But as you pointed out, maybe I just jumped the gun and I'll get that from next chapter -- not that this series have never explained away my criticism in the following chapter with some reasonable explanation before.