The
thinking being referred to is thinking by the players. The PCs can't have metagame thinking unless you're playing a game like Over the Edge, which has a self-referential dimension within the fiction.
I was going to post a reply to this but then saw that @
iserith posted exactly what I would have done.
All I would add is that it's not true that a GM gets to adjudicate every declaration of "I recall such-and-such." For instance, if during a session of play the PCs met a shady broker at the merchant's house, and then the next session one of the players says (in character) "Remember that broker we met - let's track her down," the GM is not entitled to call for a INT check which, if it fails, prevents the player from making that suggestion.
Contrast: if the player recalls his/her PC being introduced to the broker, but has forgotten the broker's name, and says to the GM "I try and recall her name," then the GM is entitled to call for an INT check which - if it succeeds - will oblige the GM to tell the player the NPC's name.