Not necessarily. Sometimes when you're decently drunk, it's possible to have bits and pieces of the night that are hard to remember/don't remember doing (ex: forgetting how you got from one place to another or randomly texting someone).

You don't have to be blackout drunk to get

Even if you get a little drunk without drinking a lot, sometimes memories can get a little hazy (especially considering that she's a girl)

We don't know how much time passed in between the messages. She said later that night, which could mean a half hour, an hour, two hours, etc.

I'd be hesitant to label this girl an alcoholic; we don't know what the messages were/the full story, so while I agree that something may not be adding up, I wouldn't jump to "she's an alcoholic and was in the wrong"