I thought I'd chip in here... I have a 1960-era #5. One of the blue ones, not a Bailey pattern. It looks and feels like a pale shadow of what the glory days of Stanley must have been, and just screams "cheap" and "not made very well." (I got it for $25.)
Even with that, I can get shavings that appear to be no more than half a wood cell thick. As you said, it's all about the way it's adjusted. Takes a bit of fiddling, but if this junker can do it, any remotely decent plane can do it.