I was one poster who suggested this at one point - and I believe I originated it, but I may not be the only one who originated it, since I don't believe it required any unique genius on my part.Someone somewhere... maybe here... suggested that Trill and Betazed were originally part of the First Federation. When the First Federation was incorporated or joined the UFP, those planets came along.
On some days I like this idea and on other days I like the idea that Betazoids were part of the Federation in the TOS era.
Emony Dax knew Leonard McCoy.

I think that contextually, there are things said regarding mental abilities in TOS that imply that Betazoids weren't part of the Federation or well known yet. But nothing definitive, so certainly, YMMV.
Emony *did* know Leonard McCoy - but I don't recall anything that says that that was before the Enterprise met the Fesarius. If diplomacy moved swiftly and the civilizations were highly compatible, First Federation citizens could have been regular visitors to Federation worlds (and vice-versa) in time for the interim between the end of the 5 year mission and the events of TMP.
Or perhaps, the reason Balok took the scary tack that he did in evaluating Kirk and company was that Federation ships were already poking around the edges of their space and it was inevitable that they were going to be in more regular contact soon, so Balok either wanted to know they were okay or he wanted to scare the bejesus out of them if his people were going to need time to prepare for hostilities.
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