Actually it could have been a fixed gear bike. When I was a kid, one of the bikes I wanted (I was 5 or so) was a sleek looking black BMX-style bike that said "NO BRAKES" on it. This was only partially true because it had the front rim brake similar to all other coaster-brake BMX bikes I saw. It was, indeed, a fixie. The only thing backpedalling would do is move you backwards (which I thought was awesome at the time. I'd been missing the ability to go in reverse ever since I upgraded from an old-school plastic BigWheel trike)