Obviously.
Just like buying a High Definition TV won't automatically give you high definition programming. You need every piece of the puzzle, from the high definition capture of the image, to the wires, to the high definition box, the high definition DVD player and I don't know what else. Oh yeah, the high definition cable service.
Same for internet bandwidth. It's like sucking through a really small straw. I can suck a lot harder than the straw will ever permit. With a bigger straw, I can suck a lot more liquid.
High speed internet is a bigass straw. However, if the information provider at the other end cannot provide fast enough fluid (or the fluid is too viscous), the big straw serves no purpose. Or if the sucker is too weak, a big straw won't help.
Does that make sense? I kind of got lost in my metaphor.
But we're all the suckers in this one aren't we? Except for those who don't have high speed (e.g. not me).