I'm sure there's another reason for why he was thrown off the bike.. can't really tell without knowing exact details or understanding what happened, but in short is highly unlikely the ABS caused it.
As the name implies, ABS actually prevents the wheel from locking and to that extent tries to ensure that the tyres don't lose friction and skid on the road. If you feel that your cousin was thrown off the bike, you most likely are suggesting that the wheels locked ( rather like the front wheel locked and he was thrown over once it dipped) which is precisely what ABS is meant to prevent.
Without really casting doubts on riding ability or experience.. let me put it this way, bikes below 250cc usually don't put out so much power that the ABS is a must have.. on bigger bikes though, the weight, power & dynamics mean it's a lifesaver.
I've been riding for over 14 years, have had a P200 for 7 of them.. have an FZ25 now & have been on friends R15/Duke 390's/VFR800's/Ninja 300/Ninja 650 .. to me for sure power is key along with the basic setup of the bike. A bad bike with a shitty suspension setup or ride dynamics or tyres & handling nature and too much power will be a basket case irrespective of ABS.
For a country like ours where we've been riding bikes without ABS for time immemorial.. it isn't as if one can't do without ABS at all.. but definitely.. if available and if you can afford it.. it's a must have.