I am not a lawyer. None of this should taken as, or construed to be legal advice.
Looking over United's Contract of Carriage upon which their passenger bill of rights are based, I found this paragraph:
UA shall not be liable for any death, injury, delay, loss or other damage of whatsoever nature (hereafter referred to collectively as “damage”) arising out of or in connection with carriage or other services performed by UA, unless such damage is proven to have been caused by the sole negligence or willful misconduct of UA and there has been no contributory negligence on the part of the Passenger
One of the planes involved in the incident to which you refer was a UA flight. They were flying per ATC guidance, therefor there was no "sole negligence or willful misconduct" etc.
That being said, to answer your given question, yes the passengers can ask for compensation. They are unlikely to be granted any by the airline, as that would set a bad precedent (not a legal precedent, but one that might affect them legally down the road). They are under no obligation to make compensation, as they fulfilled the contract between themselves and the passengers. The passengers were safely delivered to their destination with little to no delay.
In my personal opinion, the airline owes nothing to any of the passengers, even for "mental anguish" as the total deviation from flight path was well within the amount that could be seen or felt due to severe turbulence.