Bullshit, on x64 all 32 or 64 bit base arithmetic operations have the exact same cost, except the 64 bit version is one byte longer because of a REX prefix. This is why 32 bits is the natural int size for x64.
Granted, divisions are rare, but that's still nearly an order of magnitude difference in that corner case.
32-bit and 64-bit addition, multiplication, comparison, logical operations etc. are in almost all cases just as fast.
You'll still need more storage on the stack for 64-bit variables. So more cache misses (and perhaps TLB misses and page faults) when corresponding boundary is crossed.