It's not so simple, they have their standards (and they hold very strong to them) but if it's not in their standards they won't bother telling anyone. For example from my understanding the vaad does not obligate a store to be cholov yisroel but you Have the choice to be and if you do they put up on the certificate "cholov yisroel". Problem is for people like myself who are very careful in cholov yisroel can't rely on this, for true the milk is cholov yisroel and the cheese gevinas yisroel, the keilim used were never kashered when the store decided to go cy. Which according to the Rama (who my rav follows in this) makes the food ossur. But there is no way to know which stores have this issue and from my understand most pizza shops do have this issue.
A bigger issue is for the people visiting and they see a sign cholov yisroel they don't think twice about the kelim I hear a story a week about this issue
(And no we don't rely on cholov stam that it shouldn't asser the keilim)
If I'm not accurate or am missing information please inform me (I'd rather be able to eat in more places then the same pizza shop every time)