When people are talking about "a small amount like for a hamburger" they usually are proposing that the merchant look at all relayed transactions -- they should see the burger purchase, and if a bit of time goes by and they don't see any other purchases from the same address, a double-spend would be harder.
So when you say, the merchant "looks at all relayed...", do you mean, a software application does all this automatically for the vendor and comes back with an "It looks good" message?
And then when you say, "a bit of time goes by...", do you mean, less than 5 seconds?
The point I'm getting at here, in a nutshell, is, can we reliably process transactions less than, say $50, in 5 seconds or less, or not?