At least compare it to running FF26, which is the overwhelmingly-likely backup plan in such a case (i.e. they were probably using FF26 before, so they continue

At least compare it to running FF26, which is the overwhelmingly-likely backup plan in such a case (i.e. they were probably using FF26 before, so they continue to use it until they have time to fix things for FF27). Staying back one version is not unreasonable. If the company has waited 23 versions to upgrade, then it's basically their fault for being in that situation. Security patches aren't always relevant; having a working browser (any browser) trumps all. If in fact there is no patched Firefox that works, but some other patched browser does work, then the more-patched browser wins. But if the only working browser is missing a few patches, big deal; use it anyway, and consider it added motivation to upgrade company infrastructure. You're not going to shut down the company for 4 weeks because the browsers are unpatched, I hope.