When I bought my bird in 2000 it had a vinyl top. I pulled it off and had the car painted. We then installed a new vinyl top ourselves. The top we put on was on the car for ten years until it was hit and parted out 2 years ago. Just to see how well it held up, when I pulled the vinyl top trim parts to sell them to someone on here, I pulled the vinyl back quite far and found ZERO and I mean ZERO issues under the vinyl.
IMO it all depends on how the top is installed, how it's trimmed, the brand of contact cement and how much of it is used and if the person using actually knows how to use it!!!!!!
We also not too long added a vinyl top to our 67 LeMans. Again, IF done correctly and all the precautions are taken I do not see where adding a vinyl top will cause ANY problems at all. Now, in saying this, yes, there is some addition care that needs to be taken, ie: when you wash the car, use an air chuck or a leaf blower to blow any water out from behind the moldings. I do this EVERY time our cars get wet anyway as it takes seconds to do but it will prevent rust issues. I do this behind all the markers on the entire car, reveal moldings, rocker panel moldings etc.
And as I mentioned above, using brand name (3M) contact cement is KEY. A lot of shops will use the cheapest crap they can get in bulk that they can spray on, quick/fast and easy. WRONG! I used 4 quart cans on the LeMans and hand brushed it on to BOTH surfaces (the back of the vinyl and on the roof). Is this a pain in the a$$ and hard to do compared to dumping it into a spay gun, YES it sure is. BUT, it makes a HUGE difference in saturation and coverage. How many shops around do you think are going to hand apply and use 3M brand contact cement? None, would be my guess. Hence the reason I tackled the project twice myself!
This is not an easy job. And if you have never worked with contact cement, do your homework! I have written a several page article on this very topic. I believe it's posted somewhere on this site. If not, I believe I have it as a Word document if anyone is interested...