It's common for 32" TV's to be 1366x768 rather than 1920x1080, it's a random pain in the ass but it's true. There are some out there that do have 1920x1080, but some, not all. TV's also can create some strange color issues when being a monitor for a PC, can take some configuration but is by-passable.
So we are ignoring this?
What he's saying is true. Not all TVs run natively at 1920x1080, so it looks like stuff when you actually set it to 1080p. A lot of HDTVs take 1080p and compresses it to 768p (1366x768), but provides the ability to use 1080p. That way they can market it as 1080p, when in reality a lot of what you see is 768p.
You're stuck with 768p, unless you want your screen to be fuzzy as stuff.