I watched almost no X-rated or NC-17 movies at all, so the movies that I saw that had cuts were R-rated.
There may have been other edits, but that's the one which tripped my memory when watching the laserdisc copy I bought soon afterward.
The studios have alternate versions of movies and some of the TV edits may have gotten into the Blockbuster stock but your portrayal of Blockbuster as being the originator for reasons of censorship are wrong.
Also, media companies censor all the time. Take a look at youtube, which will not allow porn, ostensibly because it'll affect their brand and image. Blockbuster was probably trying to do the same thing to keep its "family" video store image. They certainly did not allow hardcore XXX porn in the store because of that, and may very well have stocked censored videos for the same reason.
Finally, you don't have to rely on just my memories. There are others discussing Blockbuster's practices of at least stocking censored films. Whether they cut the scenes out of those movies themselves or just bought censored films is immaterial. The fact is that their customers had to watch censored films. That is a fact supported not just by my memories but the other people who talk about this happening, some of which I linked to in my previous post.
If you are really interested in getting to the bottom of whether they censored or not, you could probably find and contact some former Blockbuster employees and others in the industry who can give you a more authoritative account of what happened.
Blockbuster was almost certainly not doing any editing itself, simply for the cost of running a VHS/DVD production workshop at that scale. Doing its own editing without permission of the video owner would have been outright copyright infringement, and they would have had the pockets and visibility to be sued for doing so.
Another thing worth pointing out: rental editions are generally produced and released before retail editions. It's very possible that mistakes identified in a rental edition could have been rectified for the retail edition, and Blockbuster in particular is unlikely to have replaced its rental edition stock with retail edition stock if such changes were made. Just because a change exists doesn't mean that one copy was intentionally censored.