I believe the poster you're replying to understands that. They're noting that the complaint about panther was curiously because they had already listed tiger, which is practically never called a panther, and not because they already listed leopard, which is a cat that is often called a panther. The statement about meaning "any big cat" I would guess to be a confusion based on the name Pantherinae for the subfamily of Felidae of which all these big cats are part. Though the puma, which as you note is also called a panther, is in the different subfamily, Felinae.

I personally just tend to avoid the word panther, because it very often causes confusion as to which cat you're talking about.