It depends on the contract - don't some universities have an IP clause (like many companies) where all work/research you perform there becomes the property of the university? They then give you limited rights to use this content for personal study, etc. This means that all work performed by the student for the purpose of the assignment is then under the university's copyright.
I suppose they could take this a step further by making students sign a confidentiality agreement for assignment solutions, which is legally stronger than a honor code agreement. I won't be surprised if this becomes a thing in the future.
I would agree that if the course faculty provide significant and non-trival starter code, then publishing the solution would be a copyright violation.
Some DMCA claims do indeed mention "The repository [from the student] contains code provided to complete assignments [georgia tech]" ([1]). But the claim at [2] does not mention this. It only says "This repository contains Georgia Tech class assignment solutions." under the section "Please provide a detailed description of the original copyrighted work".
If the solutions have been copied from a set of solutions published by the university, they will have copyright. If the solutions are the students own work, then they won't, and this is abuse of the DMCA.
For the sake of a mind game assume that assignments and solutions can be copyrighted.
The mind game is: The assignment is most likely produced with a solution, but published without (lets say else it would not be 'assignable'). For deterministic solutions, could you copyright it without publication?
If that were so then I would agree (although, depending on how much code is in the skeleton, it might not contain enough creativity to reach the threshold for copyrightability). But didn't sound like what's happening in this particular case (the wording is a bit ambiguous ... maybe deliberately?):
> I am part of the Georgia Tech [private], and I have found code solutions for a class at Georgia Tech. Whenever student turn into their code assignments they agree to the Georgia Tech Honor Code stating they are not cheating or allowing others to cheat by sharing Georgia Tech’s assessment materials. The assignment materials were provided to students so that they could complete their tasks and isn't to be shared with others.
I suppose they could take this a step further by making students sign a confidentiality agreement for assignment solutions, which is legally stronger than a honor code agreement. I won't be surprised if this becomes a thing in the future.