I'm surprised Doohan and Gene were such good friends after that, unless Gene spun some yarn about it being a Network decision or some such.
It's the passage of time and other things (like wanting to make sure the fans push for a revival, keep the revival going, etc. There's also th issue that actors in general try not to 'burn bridges' with producers regardless of what the Producers do; as you never know when said producer may have another job/role for you.)
Look at William Shatner and Leonard Nimoy. When the series was in production, they weren't all that friendly towards one another - and Nimoy got it into his head that while Shatner got top billing; his character of 'Spock' was the real lead/star of the show fans came to watch. Also if you believe William Windom's report of Shatner and Nimoy on set (he's one of the few guest actors not really taken by the aura of 'Star Trek' and saw the stint as just another guest TV role); Mr. Windom has said BOTH Shatner and Nimoy were line counting; and going to GR with trivial stuff, etc.
In the end, in the third season it was settled by a meeting with GR in which GR grudgingly indicated, William Shatner/Kirk was the 'star' of Star Trek.
But my point? All the above didn't keep William Shatner and Leonard Nimoy from forming a real friendship in the later years after Star Trek.