I believe the person who said that was actually confusing "stock phrase" with "set phrase" (or "fixed expression").
A "stock phrase" is, as your link suggested, some phrase that has come to be commonly used or associated with some particular person or group of people. The term is also sometimes also used to mean "a standard response" or "the default way to say something".
On the other hand, I suspect what was actually meant in this case was a "set phrase", which means a particular combination of words that has come to be used frequently in that specific order, as a common way of saying a particular thing.
Some set phrases have actually come to have a meaning of their own, different from their actual literal meaning (for example, "red herring"). Other set phrases mean pretty much the same thing that their literal words mean, but they are used often enough that either they seem less strange than they would normally, or other options sound more strange than they would be normally, just because that one phrase is used so commonly.