Hello,
you are probably on the right track with your assumption that this behavior has to do with the built-in cable diagnostics and loop detection mechanisms. The fact that the LEDs turn green when a PC is connected usually means that there is activity detected on the link.
I couldn't find much more information than what the data sheet offers. It would be interesting to know if that changes with the cable category you use (5e/6/6a/7), so if you have any of those lying around, you could test if something changes...