Anonymous user filing out a profile unintentionally remove themselves from groups
Checkboxes are inherently a confusing html element, because when not selecting them, no value is sent (i.e. not even a null or empty placeholder value). So I can imagine that the core code that this is using is trying to handle that kind of situation from other contexts. 

If that analysis is correct, then I suspect the empty box is triggering an unsubscribe, and that unsubscribe is getting merged.

To be fair, in some worlds, that might be the right answer - e.g. if that contact was authenticated when filling in the form, it would be checked, and actively unchecking it should remove the contact from the group. I'd bet you can find an issue of a description like "unsubscribing from a group via a profile not working".

Given your observations, I'd say that an anonymous contact should not be generating those unsubscribes, and if you can figure out where this code happens, it could be improved.