Here's a counter-example. We accidentally fed formula with cow milk protein in the middle of the night once after switching to a different formula (it was the middle of the night, we were sleep deprived, the bottles looked the same in the dark, and we hadn't purged all the old formula yet). His symptoms returned immediately for a couple days until it cleared his system.

I know this is anecdata but seeing the immediate change and having a very easy experiment to test it with if the child is eating formula makes me question the study.