This seems to be borne out by the events of Chapter 79:

Albus said heavily, "A person who looked like Madam McJorgenson told us that a single Legilimens had lightly touched Miss Granger's mind some months ago. That is from January, Harry, when I communicated with Miss Granger about the matter of a certain Dementor."

Even if Hat and Cloak is Quirrell, the job had to be done the hard way, without Legilimency.