Actually, it is more complex than that (sometimes). An original U.S. theatrical print of Rambo: First Blood Part II or Angel Heart wouldn’t have that Carolco logo, it would actually have the old TriStar Pictures logo - and I believe that’s what appears on the modern home releases, too.

To get that Carolco logo in higher quality, someone would have to find some European print. (And I don’t even know which countries would have had it at the beginning, and not replaced with the logo for that country’s distributor.)

Interesting topic, though. Most complete film prints I’ve seen of movies (at various theatrical revival screenings) keep the original logos. When the studios made new prints to rent out for screenings, they generally didn’t go to the trouble of replacing logos. If they didn’t make the print from an element which already had the logo replaced (I’ve seen a print of Caddyshack with the later Orion logo, just like the later video releases), they just left it. (Actual re-releases are a different story.)