The finished elevator does not need to be anchored at the equator.
The guy that heading it up picked the equatorial eastern Pacific for the reason I stated above. No bad weather, no shipping lanes, no flight paths.
Actually, I believe it does. If it weren't you would need another one at an equal distance form, and on the other side of the equator.
Even if it didn't, the satellite does however need to be directly over the equator. And for every degree off the equator the anchor point was, it would add a great deal of length to the "cable". It just wouldn't make any sense not to have it on the equator.