But can't the same be said for Rolex as long as you're not after their more popular stainless steel sport models?

While not "easy" per se, you could probably score a precious metal or two-tone Rolex at a dealer without a ridiculous amount of difficulty. I'd say you could get a SS Oyster Perpetual or DateJust (barring certain exceptions - i.e. the Tiffany dial) without too much difficulty too, unless things have changed drastically in the past few months.