For what it's worth, plenty of FFT enemies immune chicken (brave loss, no, but chicken yes). A lot more than immune blind/slow/silence, for instance. (Slow, secretly badass in Final Fantasy games.)
Even as far as extending S3 status immunity goes (reminder: it only blocks 4 status effects, out of 6, which is one of the least impressive claims to "full status immunity" I've ever seen), extending it to petrify feels weird. Petrify's a lot like instant death, after all, one of the things scarves explicitly miss. I can see saying it's more akin to paralyse, for all that I don't really agree.