Picking different bits doesn't solve modulo bias. This is more likely a memory of the warning concerning the low quality of the randomness in the low bits (e.g

Picking different bits doesn't solve modulo bias. This is more likely a memory of the warning concerning the low quality of the randomness in the low bits (e.g. in LCGs where it always alternates in the lowest bit), or the fact the high bits of rand(3) were often zero due to a small RAND_MAX.