Probably not a red flag on the car - more likely a red flag on the dealership for not knowning what there are selling, servicing. The 1998+ North American market Corollas all use a timing chain instead of a timing belt. If the engine code is 1ZZ-FE (will be on a tag on the cylinder head, side closest to the serpentine belt) - it uses a timing chain.
Correct, normally the timing chain will last the life of the engine. The lifepan on the timing chain all depends on previous maintenance on the car, how it was driven, and a little bit of luck. Timing chains on the 1ZZ-FE engines have been seen running as short as 40K miles (owner ran it low on oil too often, stretched the chain out) to over 300K miles and still counting.
The serpentine belt on the other hand, should be changed on a regular basis for piece of mind, but even they can last well over 60K miles. For my driving conditions on my 2002 Corolla - I've run my serpentine belt over 90K miles before it started showing too many large cracks, wear on the belt.
If in doubt - ask for a Carfax report and have the car inspected at an independant garage (one that specilizes in Toyota or are very familiar with this family of engines/drivetrains) or trusted Toyota dealership.