Keep in mind that there is a nice theory about not being able to lie in parseltongue.

This line reminded me that Quirrel's frequent transitions from man to snake and back seemed odd to me when I was reading. I went back to see if any of what he said after transitioning back to a man was a good candidate for a direct lie that he couldn't tell as a snake. But I didn't find anything. Most of what he said was phrased as speculation, rather than direct statements.