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"Related to that, if the FCC refused, what would stop a fully owned Amazon company based in the small country of Togreenze doing the launch instead?"

This is the only part that has a satisfactory answer. Nothing would prevent them launching the satellites from Togreenze, but they would then be prohibited from selling communications with the satellites in the U.S., where they're presumably looking for customers. The FCC regulates any communications equipment in the U.S., so if they say no to the uplinks to the satellites, the entire domestic service would be cut off and no profit for Amazon. If they're hoping to make profits there, they'll get that approval before the expensive launches. If they don't intend to sell the service to anybody in the U.S., they're free to ignore the FCC as they like.

The fact that this is the only restriction that affects these companies is not good. The FCC is not an expert on whether something is a bad idea in space, and it obviously has no jurisdiction over international activities or input from international governments.