Does the second source have the 80s Fox logo and fanfare? (Not the one on ESB and ROTJ, the long one that was on non-SW Fox films in the 80s.)
If so, it's most likely the same transfer used on that rental-only tape (and on the standard '82 VHS/Beta as well). Check the macrobinocular shot, whether it's cropped like the '82 VHS/Beta or squeezed like on the LD/CED and on HBO.
Another way to tell if it's copied from the official video is to check the end. Fox videos had the FBI warning at the end of the tape rather than the beginning, so if you see one at the end of yours....