I think that with close friends, you can tell them as much or little as you want, to give them a heads-up that sometimes you'll want to see them and if they could make an effort to see you in non-X related circumstances, that would be great. If a good friend of mine told me this, and the other person was only acquaintance-level, I'd choose my friend most of the time. If both people were the same 'closeness' to me, I would still invite them both to bigger gatherings, but make sure to see my friend separately as well.
But if it's someone who *isn't* close, I think unfortunately it's overall better to not say anything. You might be absolutely completely in the right, but an acquaintance isn't going to know who to believe, and it puts them in a really awkward situation of 'choosing' when they are effectively 'choosing blind'. Sometimes putting other people in the middle is inevitable, but I don't think this is usually one of these situations.