@coolBud
Find the contact info for your local district representative & write him dsecribing your situation. Not all of em' reply but its worth to try, give a shot. I am not sure if they offer help to foreign non-immigrant visa holders. Also, keep in mind that you might not need to go through all these hassels, this is an extreme scenerio & it worked for me. Wish u good luck for ur parents visit.
@ alti,
The reason i said nara pramanit is that you got to establish relationship between you & your parents, right? Well, in my case, i had one of those from back home municipality where they attested me & my parents pic all together on a same page. I dont rememebr using birth certificate, but might use.
And about baby thing, that what i found out doing lil researxh when i was applying for ma parents. You might be right cuz I am a layman, not a lawyer !!
Sorry for late reply guys