At this point FD personnel don't know whether Titanium is above or below Plat, so this level of nuance is likely to fall beyond their reach (and very likely that of their management/ownership). The state of FL has long had a tax exemption option via either a certificate or a photocopy of a gov credit card. Holding a gov credit card is not a qualifying requirement for a gov rate, however. I have several hundred SPG/Marriott nights in the state of FL under my belt, and I've only ever had to engage in debate on this a couple of times over the years (I've always ultimately prevailed in arguing the difference between qualifying for the rate via a government ID versus needing a government-issued CC).

So there's that last part to be considered, OP - do you at least have a CAC or something along that line to demonstrate that, although you may not hold a gov CC, you are at least affiliated with a government agency? If not, the hotel was right to turn you away. If so, they're confusing that which qualifies for a gov rate vs. that which qualifies for tax exemption. This is a FL/property issue more so than it is a Bonvoy issue.

Edit: In re-reading your original post, it's clear that you (OP) do indeed have some form of ID versus just a letter. So the hotel FD staff has been given poor direction from their management chain, apparently.