Grammatically speaking, it's fine.
Consider "She's richer than he", which is an ellipsis for "She's richer than he is". No-one seems to remember that these days, so everyone (except aristocrats, lawyers and Classics teachers) says "She's richer than him". For the same reason, "I am he" / "This is he [who is currently speaking]" / etc. sounds weird even though it's correct.
( .Yeti. El amor en los tiempos del cólera, Thu 15 Apr 2010, 12:14, 1 reply)

But in this case
It's as simple as "to be" taking its object in the nominative, in English. Which is why "Who's Who" is a grammatically correct reference book title - despite a resilient rump of punters who insist it should be "Who's Whom".

I agree about the "taller than I [am tall]" sort of thing generally - using my own favourite example just to back up yours.

The one that always annoys me is "correcting" me to I in a compound object. "Sheila gave great head to the Pope and I." No she didn't!

Also, Whitney Houston: "It's the second time around/For you and I boy!"

No. It. Isn't.

She's a complete skank and I've never been near her.

The test for this one - remove all other parts of the compound object, and see how bad it sounds. "Mr. Kipling baked some excellent brownies for I!" The dialect, far from being "proper", makes it sound like they'd be full of ganja.
(snopesthetruth, Thu 15 Apr 2010, 13:00, closed)