The only think that damn hard to explain is them being members as far back as the late 23rd Century, if not further, and it being such a shock in "The Host" that Trills are joined with symbionts. (Then again, considering DS9 basically ignored everything about that episode except for that basic premise, maybe we should too).
They wouldn't necessarily have been members since the 23rd century. While the Trill were certainly known to the Federation back then, it's possible membership didn't happen until sometime in the 24th century.
Come to think of it, Earth might be debatable. Has anyone outright said "Earth is a Federation member" in those exact words? If not, that's not canon either.
The office of the Federation President is on Earth, Earth was one of the Federation's founding worlds, and the Federation's charter signing was on Earth. That's enough canonical evidence saying Earth is a member of the Federation.