Foreign residents can as they are resident but need a long term visa. Tourists or UK visitors cannot. A letter of confirmation from a pal or relative says "Aye Greg is bunking here for a few days" is not going to work. :-)
DTV_Begpacker You are speculating. Not saying it will not change. You said it "probably" will. How are the embassies going to conduct these background checks for DTV if they do not do them now for other visas?
Exacttly this. Singapore for example need to be a citizen or long term visa holder. UK and much of UK too. In fact even as a British passport holder I can not apply in London as i do not live there :-)
DTV_Begpacker There are no background checks though. The only background checks are got O-A and the Elit (I think) and then you supply your own police clearance. The Embassies are not doing any such checks.
You can try and lie on your application and take the risk but must accept if you are caught the DTV will be rejected and it may effect further applications.