43.064 6.6.4.8.2 says that the Immediate Assignment is transmitted on CCCH if there is no PCCCH, i.e. it doesn’t specify AGCH or PCH. 44.018 is pretty much the same.
I tried sending the PDA on AGCH only and PCH only just to verify that the MS responds in either case, and the MS doesn’t seem to care which one it gets the message from. Also my logs show that the problem happens when the assignment goes on AGCH (and also PCH, but mostly AGCH is used because of logical channel sequencing).