Unless the other tires are badly worn, it sounds like a "fear based" sale, yes. Toyota doesn't seem to have any specific recommendation beyond saying that on AWD if one tire fails and the others are "significantly worn", then replace all four.
But at 12K on the tires, they should have plenty of tread left.
I'd say, to be safe about it, replace the bad tire with the identical brand and size, or if you can't get that tire, then replace the two on the axle with the flat, again, making sure those two news tires are the identical size as the 12K ones on the car already.
I think replacing all four is a waste of money on a MODERN AWD---the older ones, it might not have been a bad idea.