I think that our pets do learn things just from watching what we do and trying to copy it.
My daughter told me about looking in her sock drawer for a pair of socks, and both her kitties were in the sock drawer, ad throwing every thing on there all over vigorously. Them it occurred to her that they looked just like she did when she was trying to find a special item in the drawer and was throwing stuff all over looking for it !
I also talked to a lady that had a parrot, and she said the favorite thing for the bird to do was to make a noise like the electric can opener, and watch the cats come tearing down the stairs to see if it was a can of cat food being opened for them.