^I think ve3609's adding to Foggia's post, i.e. "Persia, for example, is a UK puppet, but I'm not sure about Turkey" so he clarified that "[T]urkey is independent," meaning that Turkey did not start out as a UK puppet and unlike Persia had no events which lead up to it becoming a UK puppet (or start out as a puppet in the scenario straight away), so though the OP doesn't specifically state either way it's safe to assume that Turkey probably isn't a UK puppet in this game either.
But more on topic: usually you can blame the AI files for diplomatic idiosyncrasies in this game. HOI2's diplomacy is woefully undeveloped, guided generally by a country-specific, relatively inflexible AI file system. I don't know how to read AI files and I don't claim to know exactly what's going on here, but I assume the related Turkey AI file forbids accepting puppet peace offers by a human USSR in the scenario (since they start so close and at war and all it'd be too easy?). It's similar to how as Germany the chance to ally Italy before the Fall of France is zero despite close ideologies and good relations in the 1936 campaign.
Note however that this is a weak conjecture based on very little evidence. I don't play the Doomsday scenario very often and as I said I don't know how to read AI files. There could be other reasons -- say, can a member of a big alliance [Allies/Axis/Comintern] ever surrender and accept puppet status without an event? IIRC Turkey is a member of the Allies in the Doomsday scenario.
Just annex and release, or plain annex.
