The biggest point to make is that typically most "Green" coolants contain a healthy amount of silicates. Its not as big an issue with a 3rd gen (since Toyota "Red" Long Life Coolant [LLC] is a LOW Silicate Formula), but it still poses an issue.
You're actually better off running something more like a silicate-free coolant like Toyota Pink or Zerex Asian Formula than anything that is closer to Dex-Cool (IIRC Toyota actually has a statement somewhere in TIS that says not to use DEX-Cool coolants in their vehicle) or higher content silicate ethylene glycol based coolants. Among a few other reasons, the Toyota stuff has a few things missing/in lower concentrations that most of the "Universal" coolants do have which can cause some issues later down the line. Again, its not as big a deal as say the 4th or 5th gens that should be using Toyota "Pink" SLLC (Super Long Life Coolant) and/or a compatible Non-Silicate, Non-Amine, Non-Borate, Non-Nitrate, based on a Hybrid-OATs technology; but it still is different than your generic "universal" coolant.
There's a reason Toyota phased out LLC in favor of SLLC, one of the many reasons is this:
That's Silicate that has actually fallen out of suspension in the coolant itself, as you can imagine that then sand blasts the inside of the engine and cooling system. Is it an issue if you flush the coolant every 30k like the old days? Probably not, is it an issue if you're trying to run the coolant 5yr/50k (like Toyota "Red") or longer? most likely, yes.
The thing to keep in mind is that coolant has come a long way from just dyed green ethelyne glycol, the additive packages and formulations are tailored to more than just "Aluminum Engine Safe." While the 3rd gens are not that new, Toyota switched to Toyota LLC back in the early 90's; so this isn't exactly a new thing.
Bottom line as long as you find a coolant that matches up to make-up of Toyota Long Life Coolant (aka Toyota "Red") It should be fine to run in the vehicle. Do not get tricked or lulled into a false sense of security just because the bottle at the parts store says "Universal;" 9/10 that's more marketing BS than actual fact these days. Not to sound like I am trying to sell the Valvoline stuff, but I did corner the factory guys and question the hell out of them as well as looked at some of the spec sheets. The Zerex Asian Formula is a great coolant for both the Toyota "Red" LLC & Toyota "Pink" SLLC if you're looking for a good alternative. Amsoil also makes a good coolant as well (again I berated them with some questions and feel comfortable enough with the data to recommend both coolants as SLLC replacements, which would mean they'll work fine for LLC applications as well.)