My Dad is an engineer, so I know what engineers do. Here are my thoughts on the subject for what they are worth:
I am ambivalent about counting math as a science, so I won’t go into that.
I thought that engineering is pretty much a professional degree in physics. If physics counts, why not engineering? Why not PA studies either. I am not sure they have solid reasons behind these, but I bet they are unwilling to bend.
As a behavioral scientist, I am baffled that AMCAS or AACOMAS, neither one, considers behavioral science as a science. True, there are few lab classes, but as someone who also has a degree in biology I can say that behavioral scientists are very rigorous in their treatment of the scientific process. More so, even than the “hard sciences” are.