AITA for correcting my aunt in front of everyone when she called my shop-bought cake homemade?

"And this one is my niece's secret family recipe," my aunt said, pointing to the cake I'd brought for our community craft group's supply fundraiser.

I interrupted: "It isn't. I bought it at the supermarket on my way here."

My aunt stopped talking, laughed awkwardly and moved to the next table. Later she told me I had made her look dishonest in front of the people she had spent all morning welcoming.

I had originally said I would bake a cake. A work deadline ran over, so I bought an $18 chocolate cake instead. At pickup, my aunt asked, "Did you manage the cake?" and I said, "Yes, got one." I didn't explain the change. I also took it out of the shop box and put it on my own stand because the box looked battered.

There wasn't a sign claiming it was homemade. My aunt's announcement was the first time I heard her describe it that way. I corrected her quickly because someone beside me was asking whether I could bake the same thing for their daughter's birthday. I didn't want the conversation to keep building on something untrue.

My aunt says she would have corrected herself if I'd whispered to her, and that the family-recipe line was just her trying to make my contribution sound special. She's upset that I left her to recover in front of everyone.

I stayed, helped serve and told her afterward that I should have explained the purchase at pickup. She wants me to apologize for the interruption too. I think the correction needed to happen, but I can see that I helped create the wrong impression. AITA for saying it out loud?