How nice of them to "Allow" you to vape which is perfectly legal despite their objections and to "Allow" you to do so "As long as" you meet their prerequisites
Well, I look at it like this: I wouldn't like to put up with one of them with bad gas so they have a point on the smell point of view- I think it's pretty much everyone's main gripe in the office (smelly handcreams, food, health drinks that seem to be made out of cow dung and grass etc...).
Also, I've made them put up with the stench of smoke hanging around me for some time (I hate the smell of used tobacco- smoke is fine, but not the "afters") so they're in a win win all round!
Tis better to be polite and bend the truth a little than incur wrath and a straight office ban. I work in HR so perhaps I can set an example to the rest of the smoking crowd!