Are you sure you don't have that backwards? Isn't Sega still in licensing hell for the music in Sonic 3 because of Michael Jackson? Isn't that why there's no HD remaster of it on iOS/Android? I know Taxman and Stealth have released a prototype of it but Sega hasn't approved it.
A lot of people have answered this, but for full background: SEGA doesn't fully own the music to Sonic 1 & 2, no. This is why, for instance, the classic Sonic 'Round Clear' music was ditched after Sonic 2 and ever since they've only ever used the one composed for Sonic 3. Same for stuff like the Invincibility music and other things that remained consistent from 1-2 and then inexplicably changed in 3 - it was because of the rights issue.
This is also why it took until two years ago to get an official Sonic 1/2 soundtrack release on CD, the composer wouldn't allow it. It's also why when you get games like Smash Bros, the remixes are always of music post-Sonic 2 - in Smash there's Angel Island Zone rather than Green or Emerald Hill for instance despite the stage itself being Emerald Hill - because if the song is remixed or rearranged, SEGA has to cough up.
They seemingly can use/print the music in its original form, though, unedited, and have done frequently. This relationship seems to be better now, though, it has to be said.
RE Sonic 3 and Jackson, it doesn't seem like there's any rights issues and to this day nobody quite knows why the tracks suspected to be Jackson ones were replaced in the PC rerelease... though it is worth noting that SEGA has also never done any official remixes or rearrangements of these tracks anyway. (Ice Cap, Launch Base, etc). Modern versions of Sonic 3, like the one on Steam and XBLA, all feature those tracks and not the PC ones, at any rate.