From what I understand, having proof of being fully vaccinated simply allows one to avoid the pre-travel testing. I suppose each country or state might have their own definitions and name for it. If it's proven that vaccinated people can gather with each other safely, but that un-vaccinated people pose a risk, it's only common sense to incentivise the vaccine. Each destination likely chooses their own rules -- so people have the option of complying or visiting somewhere else.

I always felt Dr. Drew was a bit smarmy.

Ummm, it does,you fool! When I worked (for only 6 weeks,on the US subbase in Rota) i had to get cholera, typhoid,and a cocktail of others...in 1974! And let me tell you, typhoid shots HURT!
What a dumbbunny!

He need to get out more, lots of countries require lots of vaccines already. Too bad he forgot how to doctor, I thought his show with Adam Corolla was pretty funny.

International travel may require immunization

Vaccinations are already required by many countries including the US upon return from a country with known transmittable diseases.
[en.m.wikipedia.org]

Well, if other countries demand it, all those who took his advice and said, "My rights to refuse," won't be travelling overseas. Dumbass.