Carfax and Autocheck are tools. Sometimes they reveal good info and sometimes they don't.
As someone who frequents insurance auctions I can tell you the clean vs salvage title isn't clear cut science. You can get a perfectly running clean salvage title (exp recovered steal) and you can look at a lump of molten steel (fire damage) that was a car with a clean title. There are many variables that go into whether they title will be salvage (can be converted into rebuilt), clean or in some cases branded junk or parts only (can never be converted).
Some general rules are once an insurance company pays out for a vehicle from either accident, flood or other "totaled" incident most brand the titles salvage.
Rental car companies and other self insured companies (or municipalities) many times don't change titles locally speaking.
After seeing what body shops repair preserving the clean title status and seeing the minor damage many salvage cars have I don't have problems with either route. I have sold both but rebuilt title always lowers the price but there are some real "steals" that can be bought salvage.
Some examples:
2006 Lincoln Navigator with 100k miles salvage title listed as non running. Inertia switch needed to be reset, serpentine belt replaced (orig broke causing fender bender) only damage is grill, front bumper cover and radiator core support. Body man bought truck for his wife for 1/4-1/6 the price of clean title local listed trucks.
2006 GMC 2500 SLT 4wd loaded (LBZ) listed as non runner with accident. Both batteries were shot from sitting (most cars sit for a few months waiting on paperwork) mechanic took out and deep charged truck started immediately and after body work truck was sold for 3x purchase price.
2007 F350 CC SB Lariat 100K miles one owner TX truck not a scratch/dent on it. Recovered steal with keys and remote (strange). Coworker bought it and hasn't done anything to it no issues. Bought it half of what local dealerships were asking for trucks with double the miles that were rusted.