An unfixed security vulnerability is still an unfixed security vulnerability, no matter how many people discover it in the interim. By refusing to coordinate with the new submitter, the new submitter does not know if the vulnerability will ever be fixed and is reasonably justified in using public disclosure.
The one case where refusing to coordinate with the new submitter is reasonable is when the new submitter learned about the vulnerability from the original submitter, which means that the original submitter has violated responsible disclosure. In that case, nobody would deserve a reward.