All of the Bonaire car rental companies I'm familiar with (Telerin, Budget, Total, and Buddy Dive) are clear in the rental contract that fuel, flat tires, and damage to the vehicle are all the responsibility of the renter. You shouldn't accept a proffered rental vehicle without verifying tire condition, including spare, as well as present and operating tools to change a flat. Most rental companies that we've used will walk you through this process during check-in. They also want you to acknowledge presence of the jack and tools in case they go missing from your truck, as you are responsible for them too.
Potential service charges should be discussed in advance. Each company may operate a little differently. The best thing to do is to ask them about these things prior to signing a rental agreement. In my early years visiting Bonaire I would have a rental company fax or email a copy of contract and any other T&C for my review before I'd confirm a reservation.
Threatening to "to give them their POS tuck back immediately" after getting a flat is an interesting tactic, but probably isn't within the spirit of your responsibilities and/or the rental contract that you signed. My guess is that the rental operator acquiesced just to keep you happy.
Some rental operators, like Buddy Dive, are clear in the rental contract that you'll likely incur lower cost for flat repair if you take to a repair shop yourself rather than having them do it for you.
On a couple of occasions, when alternate vehicles weren't available, I've pointed out worn tires during check-in inspection and negotiated a gentleman's agreement that the rental company would pay for flat repair if it occurred. I also carry the inflator discussed previously, but have yet to actually use it. In 26 weeks of renting trucks on Bonaire I've only had one flat, and that was discovered and changed in the morning outside our villa.
I've never had a problem in four prior trips, nor have the people I dive with who have been renting trucks every year for many more years, but this is our first experience with this particular company, whose trucks (our group rented two) seemed a little less well maintained than Buddy's with which we were familiar.
I didn't mention it earlier, but after the service guy came out to help us and HE decided it was too difficult to change the tire, the guy got in the truck and pulled it farther off the road. Guess what? When we got home we found an email from the company telling us they planned to charge us hundreds of dollars for an entire new wheel because the rim was allegedly damaged from driving on a flat. That is what enraged me--not so much the original service call fee.
I can understand and accept the renter's responsibility for flat tires when I'm renting a normal new-ish car where the roads are good, etc., but it surprises me that the terms are the same for a truck with well-worn tires and rusty parts to be driven on barely paved roads and parking areas full of broken coral in the Caribbean. I would imagine tires get worn very fast in those conditions.
It was bound to happen sooner or later, and I am now better educated. Thanks.