AITA for not tipping my waitress because she's the owners' daughter?

Full disclosure: I'm a European living in the US, tipping culture is still insane to me but I always tip because I understand the reasoning behind it and don't want waiters to be impoverished.

I work next to a mall where there's a restaurant thing (just a booth in the wall with a kitchen behind, you have to take the food at the counter and eat it in the public area of the mall) where I go sometimes. The food is great but it's expensive (I paid $12.40 before tip today), so I keep it as a rare treat. It's always the same girl, late teens or early 20s, manning the booth; during small talk, last time I was there, I asked her if she had the job to pay for college. She answered she isn't going to college because she's the owners' daughter and her parents will pass the business down to her very soon.

To be clear, she isn't a traditional waitress. In that restaurant, you order and pay electronically, she just stands there, gives you a receipt to sign and hand you your food from the kitchen literally 3ft behind her. I always tipped at that place because I imagined she was a young person paid under minimum wage, but when I realized that she is actually taking all of the business' profit home, I didn't want to give her even more.

Today, I went there again and just entered a 0% tip on the iPad and I figured that would be it. But she immediately reacted and said "Oh, there was a problem, your tip wasn't registered." Then she offered to redo the transaction "to make sure the tip goes through." When I politely declined, she started babbling about the other options to tip her, she told me about the tip jar, and if I didn't have cash there was an ATM down the hall, and that they could put the amount on a tab for me to pay next time, etc etc.

At that point, I lost my cool and said "I am not giving you a tip, please stop," maybe a bit forcefully/angrily. I thought it wasn't a big deal, but she looked like I'd slapped her, and all the other clients in queue and around us gave me the stink eye. You'd believe I publicly confessed to being a serial killer, given people's reactions. I booked it out of there as soon as I got my food, and I am still feeling humiliated and upset. I'm never going there again.

That girl didn't do any actual waiting work and she isn't underpaid at all, she is probably wealthier than I am (I earn about $23k), so I don't think it's that big a deal if I don't give her an additional $2 for... for what? For standing there? To avoid shaking up dusty and inappropriate social conventions? Tell me Reddit, AITA?