I've heard it reported that among the "normie" category of humans, having an alcoholic drink together often serves as a sort of social ritual, is regarded as a sign of friendship offered and received, and can even have absolutely nothing to do with drinking until intoxicated.
Go figure.
Seriously, I wouldn't overthink the issue. It's like if you wanted a coffee after lunch and invited your friend to have a cup with you, and felt perplexed when she turned you down.
If your friend knows nothing of your struggles with alcohol or your efforts in recovery, I can see no reason to suspect anything ominous about her request or her reaction to your turn-down.
As others have said, the important thing is that you handled it gracefully and didn't drink.