Small Stack vs. Big Stack

[jason1990]

In "Getting Started in Hold 'Em," Ed Miller writes (in a centered gray box for emphasis -- that is, this is a key point):

"Big stacks hold no intrinsic advantage over small stacks in cash no limit hold 'em games."

Does this mean that if I buy into a game for $200 and everyone else has a million dollars, then I shouldn't care? When I think about this, it just seems like common sense that I shouldn't care. After all, they effectively only have $200 each, from my perspective. But this means that when cardrooms put a cap on the amount you can buy in for, they are not actually offering anybody any protection. In fact, there doesn't seem to be any reason (other than perhaps psychological) for them to restrict the buy in.

Furthermore, I recall someone quoting Doyle Brunson as saying (and I'm paraphrasing here), "No limit games without a maximum buy in are the only true no limit games. Everything else is just spread limit." But in light of the previous considerations, this seems to be just nonsense.

Is my way of thinking about this correct, or am I overlooking something here?