When I say "JSON didn't exist", what I mean is that it wasn't popular or known to us when we were working on YAML. So, please excuse my sloppy wording. For me, the work on what would become YAML started with a few of us in 1999 (from SML-DEV list). In January of 2001 we picked the name and had early releases. It took a few years of iteration before we had a specification the collaborators (Perl, Python, and Ruby) could all bless.
Anyway, with regard to Crawford's excellent work, JSON. It is a coincidence that YAML's in-line format happened to align. Although, it's probably because of a "C" ancestor, not JavaScript. The main influence on the YAML syntax was RFC0822 (e-mail), only that from my perspective, it needed to be a typed graph. In fact, we documented where we stole ideas from, to the best we could recall at that time: http://yaml.org/spec/1.0/#id2488920.