Well, you obviously have to define "long" and "any" in that sentence. The famous xkcd cartoon evaluates a four word "phrase" (four common random words) as 44 bits of entropy. But he's not comparing it to a random alpha-numeric string, he's comparing it to taking an uncommon word and doing a couple of letter substitutions to defeat complexity requirements.
A real random alpha-numeric password (what I get my password manager to generate, since I don't have to remember it) 12 characters long is more like 70 bits of entropy. You'd need 6 random words to match that. Essentially for every 2 random alphanumeric characters you need another random word.
If you read 128 bits of data from /dev/urandom, and then map the result to a space of 2128 possible passwords, then it doesn't actually matter what the possible passwords are, as long as it's a one-to-one mapping.
