I remember that line from Covert Affairs as well - and yeah, that has always made sense to me. Among other things: it stops their agents from being honeytrapped if they already have someone who is also in the know; it makes for a far stronger relationship which has strong benefits for the psychological wellbeing of the agent, that they don't have to continually lie to their partner and on a really bad mission they can actually go home to someone who understands at least a little; much less hassle if an agent accidentally lets something slip, because again, it's to someone already in the know; on a resources angle, the partner's already had the background check done.

It's always been my head!canon that SHIELD doesn't have frat regs at all, not only for all the reasons I just gave, but because SHIELD doesn't just recruit the best of the best, but the best of the best of the best. You don't even get recruited in the first place unless you are already A) smart enough to know that getting involved with work colleagues is a bad idea for you or B) professional enough not to let it affect your job performance, whether the relationship is going well or sinking.

So yeah, in my H!C, no one really cares if Clint and Natasha are fucking each other blind, except for gambling purposes - or, y'know, the surveillance team runs a deep underground black market porn ring featuring them in 'action'.
(and Clint and Natasha have sex while undercover/in the field whenever reasonably possible because they know exactly how hot and bothered it makes the surveillance nerds, and they secretly like putting on a show... OH CRAP! ZOMBIE PLOTBUNNY! RUUUUNNN!!!!)

(oh, and on another note: the subject line's from 'How' by Lisa Loeb, right? I love that song!)