Are the Director and Tech Director student or staff? Why does a T.D. have any input as to stage management staffing? Are there moving wagons or trap doors or flying that the SM would have to call, which makes it a safety issue?
If they are anything like my theater program, there isn't necessarily a head of the stage management department. My school had the Lighting Professor in charge of Stage Managers. It might just be the way their department is structured.
Back to the question at hand: If you are teaching them, and in your opinion the SM can handle the show, you should just hope that the Director and TD respect your decision and expertise in the craft. If you vouch for the SM and they still want to make the switch...I don't know what to say. They are obviously missing one of the lessons I learned in college: Fail here where it doesn't matter vs. in the real world of theater where it matters more.