Suggesting changing the slogan to get it right seems odd when, according to this poll, it's the most popular slogan so far...
I think, as has been alluded to earlier, there is a crucial difference between a slogan associated with an initiative, and a detailed description of what the initiative is trying to achieve. It's never going to be possible to describe exactly what the intentions are in a few words. But equally, having some sort of slogan evidently helps things to stick in peoples' minds. It takes 1 click from the UKC home page to find the phrase, "Please don't remove any active scientific, rescue or digging equipment".
It seems clear that the intention of the scheme is to encourage people to not just ignore rubbish, but to actively do something about it, so of course emphasis is therefore going to be on the side of doing something rather than nothing.
In a more general context, if you leave a pile of stuff anywhere (above or below ground) then you have to consider how others may deal with it. If you think it could be seen as rubbish, surely it's worth leaving some relevant info with it?! If you don't think it could possibly be seen as rubbish, then there's no problem. If one of the outcomes of this is that some information tends to be left with digging gear, surely that's no bad thing in the long run?
A group of people have put a not-insubstantial effort into initiating a conservation scheme that many people seem in favour of. Let's not focus time and effort being picky about a choice of slogan.