The dictionary.com definition of "hydroponic" is:
"Cultivation of plants in nutrient solution rather than in soil."
It's important to note that mushrooms are not plants, they are fungi.
Hydroponic mushrooms are normal shrooms. It's fairly common for people to call mushrooms that have been grown
indoors "hydro" because people associate that word with indoor
cultivation, having a high quality and being excellent in appearance
(which is typically the case with the expensive strains of marijuana).
Psilocybe cubensis mushrooms are
traditionally cultivated using compost, straw, grain substrates or brown rice flour "cakes" -
not a liquid solution by itself. Thus they are not grown
hydroponically.
Calling them "cultivated" as opposed to "picked" would be the accurate thing to say.