That legal advice wasn't even worth what it cost.
Of course you can post your videos on youtube.
Any suggestion to the contrary is incorrect.
The myth, which is often quoted on forums goes back to an incident in March 2015 when one FAA official overstepped his authority.
The FAA clarified the situation soon after.
Read all about it here:
FAA Admits That They Shouldn't Be Ordering People To Delete Drone Videos
And that's another opinion that isn't correct.
The FAA and CAA aren't the who-can-sell-photos-&-videos police.
Their business is aviation safety.
They are concerned about unlicensed commercial flight.
The flight was completely legal and done for recreational purposes.
Having the good luck to take photos or video on a recreational flight that someone later wants (and maybe will even pay for), doesn't retrospectively make a previously legal flight illegal.
To see the FAA's opinion on this, read this post:
Incredibly lucky new Phantom owner
If the video is good enough for the university to use, it's good enough for them to pay for.
Don't give your work away.