The Resident Evil 1 remake may not be the best example. When the remake was made for the GameCube years back, there were many additions to both the story and game play that were not there in the original game.
Such additions being the story of Lisa Trevor and her family, to fit in with the later story elements that were not present in the original game. There were several new areas that were not present originally. Tiny additions to some of the game play were the ability to quick turn, and to better fend off an attacking zombie which weren't in before, but make sense to be able to do for this type of game, and even a section where you can play as Rebecca for a bit if Chris gets poisoned in the boss against the giant snake was added.
There are even more changes that I just don't have the drive to bother listing, but the reason fans didn't complain was not because there wasn't any changes, but rather because the changes were implemented well, and made the game better for being there.