A Theory about Pince and Snape (and Filch)

Remember back in OOtP when Mundungus turned out to be the "hag" in the women's black robes and the long black veil? I always expected that to come back into the plot somehow....

I think Irma Pince should be rearranged into "I am Prince" instead of "I'm a Prince".

Harry notices Irma Pince hanging around Filch in HBP. In previous books we never see them together. We have, however seen Snape and Filch hanging around and talking to each other many times, confiding in each other. No, I'm not trying to ship Snape/Filch...that would be disgusting... come on, Filch with anyone is a sick idea :)

I think Snape snuck back into the castle through a tunnel passage and is impersonating Irma Pince. He's got the same veiled outfit that Mundungus wore at the Hog's Head, and who knows where Pince is right now.

Notice that when we see Filch and Pince we don't hear their conversation. The trio assume love is in the air, but why?

If Snape were taking Polyjuice potion (when "Pince" is seen, sans veil, with Filch) then we would know something's up as soon as the trio (probably Hermione, since she's in the library all the time) notices the voice is not quite right for the librarian.

At the funeral, when we can't really see Pince under the thick veil, they just assume it is her. It might be that Snape couldn't take Polyjuice Potion this time (either no time to brew it or couldn't get more hair from Pince), so he borrowed the veiled outfit from Mundungus, who might not yet have known what Snape is now accused of, namely killing Albus Dumbledore.... Besides, Mundungus is a shady character and might not care what Snape used it for....

Of course, it really could be Pince with Filch the first time, and Snape impersonating her only later at the funeral.

This would mean that Snape attended Dumbledore's funeral....