Well, they're correct in that the TSB and fluid was made to solve a particular problem as I previously mentioned too but it's also advised for severe operation too, such as towing. It's hardly "vague" or "confusing". As for that TSB being "old", yes it's specifically for '98-'00 AWD and FWD auto trannies and it came out when those cars were still under warranty. Volvo usually doesn't update their info once those cars are older, out of warranty. We've used that fluid and experienced its curing effect for many AWD trannies since the TSB first came out. We've never used it in any FWD trannies.
We have had a few customers request synthetic ATF and IF one wants synthetic ATF, THAT's what Volvo recommends so I personally wouldn't try anything else being that I don't know how it'll hold up. I have read here that some have used other brands, better or worse? I wouldn't mix any synthetic with DexIII either.
Will synthetic ATF extend the life of your new trans? Doubtfull IMHO. I use synthetic engine oil in my car but not synthetic ATF because I just flush my ATF periodically and my type of trans doesn't have any premature failure problems so I don't worry about it. I also don't tow anything with my car.
If you've never flushed the original trans and its fluid was NG (likely), that's probably why it failed. I've seen that happen before but most go further even with neglect.
I'd advise just flushing your new trannies ATF periodically. Many here have different opinions on just how often but with my cars, it's about every 2 yrs or 30K miles. The fluid should be redish in color, not brown or black.

BTW, your "new" trans is not really new, it's re-built. To date, we've not seen problems with any Volvo reman. trannies so I wouldn't worry about it.