battery and alternator caused spin out on lincoln aviator?

i was getting off a highway exit ramp today going about 40 mph and my lincoln suv spun completely out of control. the steering wheel locked and the car did two full turns before slamming up against the curb/guardrail. the car would not start afterwards at all. i am completely fine but have just heard from the mechanic that the battery and alternator both need to be replaced. is this a reasonable assessment? i had no warning lights come on before this incident and no indication that anything was wrong. i had my oil changed three days ago and he said i may need a new battery by the next oil change? trying to decide whether to trust the mechanic or tow AGAIN to dealer
you are right, it did just get more difficult to steer! i am obviously not a car person :) so, you are saying that the alternator would have given me a warning light? it was such a scary experience that i don't want to repeat but w the battery just checked and no signs that anything was going wrong, the alternator/battery combination seems strange even to me. i'm trying to avoid the cost of a second tow (dealer was closed today and i had to get it somewhere) but will pay for it if it's worth it.