The fact that details of the issue _will_ be disclosed publicly is an implicit threat. Sure it's not an explicit threat, but it's definitely an implicit threat. So the demand, too, is implicit: fix this before we disclose publicly, or else your vulnerability will be public knowledge.
You should not be threatened by the fact that your software has security holes in it being made public knowledge. If you are, then your goals are fundamentally misaligned with making secure software.
I don't think that you understand the point of the delayed public disclosure. If it wasn't a threat, then there'd be no need to delay -- it would be publicly disclosed immediately.
