I've been in situations like this many times. The events I ride are either non-competitive for the most part or they have separate categories for race and sportive entries.
Occasionally I've found myself solo and encountered a group that I want to join, to benefit from their draft. More often, I'm with a friend and we want to merge with another small group for everyone's mutual benefit.
I think communication is key, as mentioned above. We always approach the group and ask "You guys want to work together?" We've had others approach us with the same question. (When I'm solo I'll phrase it , "You mind if I join you?) I don't recall ever getting a negative reply.
Quite often, I'm not able hang with them for long. I'll ride with them for maybe a few miles or sometimes for 10 or 15 miles and take my fair turns on front, but I'm not very strong, so eventually they pull ahead and I cannot keep pace. I've often talked with groups at the next aid station, checkpoint, relay exchange, or at the end of the ride, and have had only positive feedback there. Nobody has ever said, "What were you thinking, trying to ride in our paceline? You're too slow. You were just in our way." Rather, it's always been something like "It was nice riding with you back there. Thanks for joining. You doing okay?"
Theoretically, there might be some elitist snobs who would take offense at a guy like me asking to join... but I've never encountered them. This might be because they were really moving, whether in the race category or just sportives with their own big group--either way, too fast for me and my buddy to cross paths with them.
Paul Barnard, I wouldn't sweat what transpired yesterday. It sounds like no harm-no foul for everyone involved.
Also, I've never been in line with a group that stuck to a really strict rotation for long. They'll spread out a little in turns or descents, someone will come off the front but not return all the way to the rear, maybe someone moves to the left for a minute to talk to a friend or grab a snack out of his pocket, something like that. I guess the kind of guys I ride with are not super serious about it, so I would not find it upsetting to see the minor irregularities you describe.