Even in light of Dutch etiquette (or lack thereof, the Dutch tend to be very informal. I know cause I live there) this is a faux-pas for sure and will have raised some eyebrows. It will probably, depending of course on the people involved but people being people, also have been the basis for some gossip and/or snarky or disapproving remarks made in private afterwards. However, "blurting out something stupid" is a fundamental part of the human experience. We've all been there; you, me and luckily also your friends. Stuff like this is not unforgivable and I would be surprised if it was treated as such. If it was, it would almost certainly be in a much broader context involving more than just this single incident.
You obviously still feel bad about the whole affair and feel the need to apologize to your friend again, but the first question should probably be: should you apologize again? I think this depends on your friend. If she has already shrugged it off, bringing it up again might not be the best thing to do. Your mutual friend might be of help here, you could inform discreetly.
If you do sense that your friend still feels hurt, or resentful towards you, you could try and "talk it out" as the Dutch say, but you'll probably want to pick an appropriate time to do so. And you should be reasonably sure she is willing to talk about it with you, again something your mutual friend could help you with. If you do, being completely honest would probably get you the furthest. I wouldn't recommend adding meaning where there is none, if you didn't think it through (or didn't think at all) just say you didn't. The Dutch use an English word for this: "brainfreeze". If that is what it was, call it that. Calling it an "honest misconception" might be explained poorly, like there is a truth to it (which, even if there was, would be wise not to mention). Mixing and matching your own words together you'd end up with something like this:
I felt really ashamed that I put you in that position. I didn't mean it as an insult or anything like that. I feel very bad about it.
Also, I wouldn't worry much about the other people that were in the room, to them it will probably just have been another weird/awkward situation that is easily forgotten, especially since you've already apologized.