The most likely reason for this is that you have copied over an earlier version of the game. GTA 5 receives regular updates, and the way GTA 5 is installed involves a smaller amount of larger files, instead of a larger amount of smaller files.
Steam, when updating, just checks if your file is different from the same file in the most recent version. if it is, it redownloads it along with any missing files. It can't download just the changes, it has to download the entire file.
Considering GTA 5 had the Biker DLC update only a few days ago, it's possible that the vast majority of files has been changed, causing them all to be different from what you have on your SSD and require redownloading.
There isn't really a way around this. In theory, you could find someone who has already patched the game, copy over their files and then do the check again, but unless both drives are really fast, that would probably take a long time, to the tune of hours.
Update: Apparently, if you move over
appmanifest_<gameid>.acf from the
steamapps directory together with your game files, Steam will know what version of the game you have copied over and know how to update from there.