Only thing I can think of is too much pressure at one time but even that shouldn't be possible. If it was really stiff it might be rotten and split but not soft nearly as a rose petal, hard and brittle.
Yes, that check valve would be necessary for the accelerator pump, else fuel returns to the carb on the accelerator squirt stroke? For the pump to work the inlet and outlet must have a check valve. The outlet valve is usually in the 2 carb nozzles, one each.