Being a "Hertz President's member" has no weight in St Maarten. The business there is in name only and is locally owned and operated. You'll get no bonus points or perks being a Hertz member for your rental on island. Just being a loyal regular renter with them does get some upgrades and benefits.
Good to know, Scuba. That just further confirms for me that there is no real advantage to using Hertz. I have used Hertz (and still do) all over Europe, the Caribbean, and North America, sometimes with individual franchises rather than corporate-owned locations. I have always had my status recognized. So I assumed it was the same on SXM.
In any case, the first time I had trouble with them was a mix-up in the paperwork. it did eventually get sorted out, but took an extra half-hour. The next year they tried to put me into something like an i10 instead of the Corolla I had reserved (none left). It was about my fifth year renting with them, so maybe it had nothing to do with the President's Circle agreement, but they did upgrade me to a Corona.