In my experience, that's not the case.
I've had three instances of bins being taken.
The first was before we got wheelie bins and I bought a metal bin, because the alternative was to put the many black bags in the yard where the children played, which didn't seem at all hygienic. I made the mistake of putting the bin out and it disappeared. The police pretty much asked what I expected to happen?!
Second instance was with a wheelie bin, on bin day it disappeared. I rang the council they said I'd have to pay to have it replaced. I was told by someone that if you reported it as a crime you got it free - you don't! - but the pcso did pop round. But by the time they turned up I found the bin, in the youth club's yard full of their rubbish! I took their rubbish out and brought the bin home after having strong words with them about taking other people's property.
Last time was in some way our fault.
We had two bins, one slightly smaller, we were granted the second bin after proving their were more than the average number of people in our household and that we adequately recycled. Youngest son was tasked with bringing in the bins, and mistakenly brought in two full size bins. Ours and one belonging to a neighbour. I returned the bin to the alleyway, and it was promptly collected by the unknown neighbour, but our bin was never returned. Council told me I'd have to pay for a replacement.
And trust me they don't take kindly to threats of dropping your rubbish on their doorstep either. Fortunately our bin men were reasonable sorts and were quite happy to take an extra bin bag or two after I had a friendly chat with them.
On the up side, since moving house, we've ended up with an extra bin. So it all evens out in the end.
