I always thought that too. I spend a lot of time outside and check rigorously. Very often I find a recently attached tick. Found a fully-engorged deer tick half-detached not too long ago - pulled it off jaw-intact. In treatment for early-mid stage disseminated Lyme again, for the third time. Certainly a hidden tax one pays living in New England...I've recently put a lot more effort into things like permethrin.
From what I understand, you're spot on with your last note. Larval stage can be extremely hard to see even when fully engorged. Adult-stage ticks (at least Deer Ticks) are the size of a large grain of cooked brown rice. I've seen fully engorged nymph-stage that rival the size of a grape...
I’ve been fortunate that all the ticks I’ve found on myself I discovered before they began feeding because I am very hairy and they tickled my hairs on my legs as they made their way up.
One other I found crawling up my white tshirt. Good reminder to wear light colored clothes when you’re out where ticks are.