I'm all for putting some kind of "Back it up" wording in the FAQ, but particularly with workplace issues a lot of suggestions may come from but second/third hand sources, or you have a strong opinion based on years in the field (e.g. my answer on Should you always counter the first offer letter?Should you always counter the first offer letter?).
There are plenty of good, sound answers that may not come with research or first-hand empirical weight to back them up, and if we don't want to force those out or have the site degrade into FAQ rules-lawyering, so we need to be careful how we approach this: I think it should be expressed as a preference rather than a requirement.
On the subject of enforcing the policy, when Server Fault redid our FAQ a while back we didn't add a "back it up" clause -- the community expectation is that you will back up what you're saying, and voting patterns favor answers that give supporting data/reasons, so there was no need to explicitly call it out (the idea never even came up as far as I recall).
That community is way larger than we are, but I think self-policing with rep & votes rather than heavy-handed deleting is a preferable enforcement strategy.