I'm not clear on what you mean by 'snappy' feeling. Do you mean there was a feedback coming from the brakes? Was it rhythmic, as in, a regular pulsing that increased or decreased based on speed? Or did it feel more random and unrelated to speed?
You verified there is ample friction material on the brake pads?
Did you inspect the brake lines? Follow the brake lines and note if there is fluid leaking from any of the connections in the lines. On the calipers, the fluid will turn to white crystal looking type flakes and only a little will be left behind.
When was the brake fluid last bled? Water in the lines can cause failure when the system is heated up, usually by braking frequently as this does not give the system time to cool down. Keep in mind, the system is designed to operate properly for the vast majority of street riding, but that is assuming the fluid is being maintained (i.e. the heat is only a problem when the fluid is bad).
Something I do on my bikes after bleeding the brakes is what I consider to be the backyard mechanic's hydrostatic system test. I pull the brake lever all the way to the throttle and secure it there using a rear wheel tie-down, though anything that can hold the lever there can work just as well (a few strong zip ties, for example.) I then leave the bike in that condition overnight. This also has the added benefit of helping to release small bubbles still trapped in the system, making the brakes feel more firm. The next day I inspect the lines to verify that fluid has not leaked from anywhere. The only place I've ever seen brakes leak from is the crush washers, but I still take care to inspect around the pistons by removing the calipers (Usually just two bolts, but follow the manufacturer's manual and be sure to torque them to spec when installing).
With the bike on its center stand, have a friend sit in the passenger seat so that the front wheel is off the ground. Spin the front wheel to verify that the brakes are not binding. Note that it will not spin completely freely as there is some friction provided by the brakes even when not applied, but usually you can get at least one revolution. If it feels particularly difficult to spin the wheel and it doesn't carry any momentum at all, or very little, then there is something wrong with the calipers, likely requiring a rebuild.
If that all checks out, you might consider inspecting your caliper, especially the pistons following the procedures in the manufacturer's manual.
As far as safety is concerned, any time you get on a motorcycle, especially an old one, there is a risk that some component may fail. I think your best bet is to find a competent motorcycle mechanic and have them inspect the system and advise them not to do any work without your approval.
I am not aware of a way for tires to interfere with braking as you describe. The brake system is not related to tires, other than to provide friction between the ground and the bike. I have had tires that were incredibly out of balance (from the manufacturer) and I have had wheel weights fly off. I've also ridden with a rear tire on the front, and I have no idea what your mechanic means by 'uneven' wear. If he means that the tire was worn more in the center of the tire than the sides, then that is perfectly normal for most street bikes because most riding is with the bike straight up and down, especially when riding on freeways, and especially on heavy motorcycles, like the ST1100. If he means that the rear tire was worn more than the front tire, this is also expected, and, again, occurs more rapidly on heavier motorcycles. If the tire has been under-inflated, then 'cupping' can happen, but usually even novice riders notice this because of somewhat unpredictable, unstable, or hesitant feeling when leaning into corners, even at lower speeds.
I don't know about the laws where you are, but most states in the U.S. require the mechanic to get approval from the customer before doing anything that will cost the customer money, else-wise the customer is getting free labor and materials.
If a mechanic were chasing down a brake problem through my motorcycle's tires, I would find a different mechanic.