Absolutely fascinating. That Professor friend of yours is indeed correct, the fact we can see the back of the limo proves that. Polaroids are as tough pretty much as a normal photo print once dry and the chemical reaction is over; so that thumb print is deliberate damage- absolutely no doubt about it. It was probably put there to hide two things - the fact the brake lights are illuminated AND to hide any ejecta from the head shot that might have been clearly visible on the trunk or even on Bobby Hargis who said he was hit with it so hard he thought he had himself been shot.
I've often wondered why Babushka lady never came forward to be identified, sounds like she was another 'plant' of many in the Plaza that day. Note Zapruder is there in the frame atop the pedestal, I could well believe Babushka lady's task was to get a shot that showed Zapruder in order to establish without doubt that Zapruder was where he said he was doing what he said he was doing. Just a guess on my part of course.
If you look at the very bottom of the photo in the centre you will see the front headlight of Hargis's bike and it appears blurred due to motion, yet just to the left of it, the rear wheel of the limo is noticeably less blurred.
This means the bike was moving faster than the limo, so that tells me that the Polaroid was shot when the limo was already braking to a stop but before Hargis and the other cop had time to react and also brake.
Mary Moorman and Jean Hill have always struck me as being honest; there is too much detail and consistency in their statements over the years to think otherwise.