Your friend sounds *not unlike* my BFF, who can be a wee bit high maintenance from time to time. Given that she's clearly so important to you I'm going to assume that this is unusual and probably grief-inspired. The part that would be really hard for me to deal with is the part where she wants you to "own up" to something that you don't even seem to understand -- something that seems to be in her own head.
That would drive me insane. So kudos to you on that front.
If I had a relationship on any kind I might talk ot her husband to get the lay of the land -- just to see if it was a good time to approach... becuase things seem s iffy and strange right now. In general I can say to my friends "I sincerely did not mean what you thought I meant -- but I apologize for not being attentive in that moment" -- or something like that. Something I can own up to because it's true... not something she's invented that really *isn't* true, but saying "you know what, in that moment I wasn't being present and I'm sorry I hurt you, that's never what I meant to do." rather than...owning up for this mysterious thing.
And, yeah, a gift/card/flowers probably couldn't hurt.
