Someone in one of the early threads (maybe the guy with the hat?) said it should be changed to East River to fit the Bronx better, but you're right Hudson River fits rhythmically. They have to do a weird extension to "of the" to make East fit instead. It's a stupid change.
I'm also not sold on the "Ya bettah believe it" bit. I know its in one of the later parts of the song but it sounds so weak thrown into the chant. Clearly they don't want to leave that large gap without music to fill it in, but what about:
New York belongs to me!
*clapclap clap clapclap clap*
A city's pride the dirty water
of the Hudson River.
New York belongs to me!
Edit: and since this is the Templados thread, you guys could help fill in that empty space by drumming to that rhythm:
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