possible plothole that have been bugging me!!

Well, it might be argued that this is not the tightest bit of plotting in the movie but I think it stands up. The cop (. . . Brian!) has taken pity on them and left them with the doctor. At the time he leaves he still believes that Martin is hurt from the accident. It was a minor incident and there is no reason for him to hang around. Would the doctor bother to ring the cops to let them know? Would the cop bother to follow up when he eventually found out? Apparently he didn't.
In any case the scene is hilarious and accomplishes its aim of establishing the growing friendship between Martin and Andy and has no other consequences to the plot. Good enough for a movie, I'd say.

My impression was the doctor just didn't tell the policeman that piece of information :)

The other two posters covered the rest, so I'll just add that this was the funniest scene in the movie, one of what I remembered best about it and how I would describe it when trying to hunt it down after seeing part of it on cable long before Amazon and before the Internet loaded up with so much information on this stuff.

Saw it originally so long ago that I didn't even realize it was Russell Crowe until I finally found it on Amazon and looked at the specs to ensure I was choosing the right Proof movie.

(edited to correct typo in Crowe's name)

I assumed that doctor-patient privilege would have prevented the doctor from revealing Martin's lie - though I don't know that it would apply in such a case, now that I think about it. More likely, the dr just let . . . Brian think what he did at first, for her own reasons - she liked him, thought it was funny, and felt superior to the police, maybe. In fact, I thought she'd already (simply) told Brian "Yes, he's blind" before he broke the "news" to Andy, and the scene we then saw was a flashback to the exam, as it seemed they would have rushed Martin straight to a doctor.

I agree, damned funny sequence!