Oh man. I just feel bad for you. I really understand her point of view because of how she found out and everything.

Look, there's nothing sexual going on, and I get that, but in the future make sure she knows when you're going on a solitary lunch outing with another woman. This is where you truly did fuck up. Royally. I slapped myself in the forehead reading that part where you just forgot.

I just casually weave it into conversation if I do have lunch with a woman, because I have this fear that an issue like this could arise, and my wife is the least possessive woman on the planet. I have literally slept in the same bed as my best female friend and my wife didn't even bat an eye because she knew from me and I didn't make it a secret OR a big deal. This friend and I lived together for a while as kids and had to sleep in the same bed all the time because there wasn't room anywhere else, so it wasn't weird to us at all, but I still made sure my wife knew. When I told her she said she didn't care, and then told me what she was getting for lunch. Doesn't matter that she didn't care, it matters that I told her.

A casual offhand comment could have stopped this whole thing from happening, because your wife could have shut down her nosy friend in a heartbeat.

I don't care if you don't feel like you did anything wrong. You need to apologize. Profusely. Repeatedly. She was made a fool by friends and now they're running the show. Better believe they're giving her all sorts of speculation about you right now, and since they supplied the information first they're perceived to be the more trusted people right now. By the time they're done you'll be labeled a cheater and maybe an abuser. That's just how rumors are. Apologize, stick to the truth, rinse, repeat. Stop worrying about whether or not you did something wrong. You made a mistake by not disclosing pertinent information in a timely fashion, but you didn't cheat. It doesn't matter more than your relationship.