All true, but getting back in to the U.S. can be a bee-yotch if you've gone to a travel-ban country, unless you can clean that paper trail.
And, yes, I was suspicious before, and aware now, about the lack of a ban to Paki in 81.
A lot of countries don’t stamp a visa in your passport, but issue you a separate travel document that is surrender when you leave the country. Pakistan wasn’t one of those, but some countries which are a bit sensitive and maybe want to reassure visitors that their stay won’t be disclosed to folks that need not know, used these separate visas. One that I know did this was the Soviet Union, and I believe it possible that Israel also issues a separate travel document.