Your brother has more leverage than he thinks.
Responsible school administrators do not waste money/time on free speech lawsuits unless (a) they are dead-to-rights certain that they will win, or (b) there is some other incredibly important issue (e.g., an innocent teacher's professional reputation as in Sagehorn v. Rogers, where the lawsuit -- even if lost -- sends an important signal).
Lawsuits are EXTREMELY expensive, not just in dollar terms (which may or may not matter regardless of the outcome; larger school districts have insurance, retainers, often even in-house legal staff) but also -- perhaps more importantly -- in staff time/energy and public relations terms.
Furthermore, there is a lot of grey area in current court precedent re: student free speech on the internet. SCOTUS hasn't made a single peep about this issue. This, combined with the above fact about lawsuits, works in your favor. Lawsuits on contentious and undecided questions tend to get national attention and can therefore take on a life of their own in school board elections, upsetting an otherwise friendly board. Top administrators know this risk. If the issue is really as minor as you're making it out to be, and serves as a good test case for student free speech on the internet, no superintendent in his right mind would risk a friendly board over some dumb internet video.
Furthermore, the circuit courts that have spoken on this issue made many free-speech-friendly decisions; in particular, the second circuit proposes a test that your brother's school will almost certainly have a very hard time passing [1, page Page 16 of 18, top paragraph].
So, I would advise your brother's legal guardian to take the following steps:
1. Write an email to the superintendent expressing their belief that this is a highly inappropriate and very possibly unconstitutional attack on their child's free speech rights. Request a meeting in person. Emphasize that if this issue is not resolved soon and in your child's favor, your next step will be to consult with lawyers.
2. If no dice, contact your school board representatives and explain that you think the administration is over-reaching. Contact them individually and, if possible, in person. A single sympathetic board member can create enough political head-aches for administration to back off.
3. In parallel, contact the regional ACLU. If you don't have luck, try the bar association. If you don't have luck, find a lawyer who provides free consultations and get a sense for how grey your case is.
IANAL, but have some personal experience in this: I had a somewhat similar issue in high school, back when the internet was just becoming mainstream. There was literally zero legal precedent on public school first amendment internet speech issues. Literally not a single case. Is this Tinker land? Is the speech happening at school, outside of school, or both? After all, you can access websites at school. Does whether or not people actually accessed the website at school determine if Hazelwood applies? Etc.
Oh, and this was also before Morse v. Frederick, so administrative reach beyond the schoolhouse doors regardless of internet wasn't even well-understood. (BTW, Morse v. Frederick probably actually works in your brother's favor, unless his video was about Hitler doing drugs.)
Lots of opportunities for the school to lose.
Fortunately, my parents were supportive and the district decided they had better things to spend money/effort/PR on than a test case on the extent of student free speech in the emerging internet age. Good thing for them, because there was an almost identical case less than 2(?) years later with a six-figure settlement against the district. Emailing that decision to the power-hungry admin who tried to suspend me was probably the most passive aggressive email I've ever sent.
[1] https://www.gpo.gov/fdsys/pkg/USCOURTS-nynd-3_12-cv-01888/pd...
BTW: my children will NEVER use school-issued laptops unless/until SCOTUS rules that Hazelwood doesn't grant censorship rights just because the speech is typed out on a government-owned keyboard.