"I was partly right"
You were, probably. The second exit is quicker when there aren't roadworks. The supplier is cheaper on the headline price. The film did come out in 2009 somewhere, at a festival. There's nearly always a salvage, and the salvage is what the line clings to at the turn. "Well, I was right that it's normally quicker." True. And?
The salvage is holding in a smaller room. You've conceded the big thing without saying so, and moved the argument onto the small thing, where you can still win. The other person can hear the move. What they wanted was one sentence about the roundabout, and what they've got is a sentence about roundabouts in general, which is true and which nobody was disputing.
The test is whether the right part changes anything. Sometimes it does. If the supplier is cheaper on the headline price and the onboarding cost is a one-off, that's a real consideration and it belongs in the meeting. But say it after the climb-down, not instead of it. "I was wrong about the total, the figures are clear. The headline price is still lower, if that matters for next year." Now the salvage is information, not defence, and people can use it.
Mostly, though, the right part doesn't change anything, and saying it is just a way of not being fully wrong out loud. Watch for the word "but". "I was wrong about the roadworks, but normally it is quicker." Everything before the "but" was the climb-down. Everything after it is the salvage, and the "but" tells the listener which half you meant. If the second half is needed, give it its own sentence, later, or not at all.
There's a pride in being partly right that's worth naming, because it's a good instinct pointed the wrong way. You want your claims to have had something in them. They did. The way to honour that is to be the kind of person whose claims get withdrawn cleanly when they're wrong, so that the ones you don't withdraw carry weight. The salvage does the opposite. It teaches people that even your climb-downs have a defence in them, which means none of your sentences quite close.