Why would we smell like smoke when we aren't lighting anything on fire? I usually vape Fiddle Faddle or butterscotch and I hardly ever have anyone say anything about smelling a lingering smell in my office. A couple times people have walked in right after a heavy vaping session and said they smelled maple syrup or vanilla, but no one has ever said they smell anything on my person or in my hair. I wear vanilla perfume anyway so the sweet scents from vaping compliment it nicely. When I say, "Maple syrup? Really? That's odd," they said, "Never mind. I don't smell it anymore," so it must dissipate quickly. My in-laws are very, very rabid anti-smoking and they used to comment on my smoking often when I did it, but not one has said a word about it since I started vaping (they don't know I vape but I'm sure if it left a smoke odor on me, they would go ballistic). I used to use breath mints and perfume and hand lotions and hair perfume, etc to disguise the smoke smell and I don't do any of that anymore, yet no one has ever said they smell smoke on me, even after I've vaped constantly with the windows up on a long, solitary drive in the car.
I would imagine that if you vape tobacco flavors heavily all day, you could have a slight tobacco scent stick to you, but it would probably be very slight and tobacco, not smoke. I think your friend was smelling himself, not you.