It's a really, really tricky subject and quite controversial. It's handed out like candy in the US, perhaps because it feels to the patient like they're "doing something", but over here it's very much the other way round as research seems to indicate it makes no difference.
Basically the main issue is by lying in bed all day your muscles go to crap and it can have negative effects on your general health in the long term as well as short term. If there is no provable benefit to the pregnancy then it's not a case of benefits outweighing the risks.
On the flip side of the coin, logically it feels like lying down would take the weight off as would taking it easy. Certainly overdoing it brings on contractions which is not great with IC.
I guess the thing to consider is if you were active and something happened, would you blame yourself?
Personally I would at least try and take it as easy as possible, and avoid unnecessary journeys on foot, housework etc. But not stay totally inactive. This is what I have done in the past.
The one time where it really would make a difference is where things are literally almost hanging out, but you'd be in hospital for that!