Yes, there is legal precedent against this that would only apply to a government employee. First, let's discuss the private sector.
In this case, you are a private employee that comes to your place of work and accuses you of "stealing the cookies from the cookie jar" which is a serious criminal offense. They wish to talk and your boss is in the room. You plead the 5th, but your boss says you're fired if you don't talk to the cops. This is legal because you still have the right to refuse to talk, you just lose your job. A private employer has the right to free association, and wants nothing to do with cookie thieves, alleged or actual.
However, in the government employ, your boss is an agent of the government. This same situation is different because the government pays the boss and the agent... so in essence the government is saying talk or be fired. This is unconstitutional as the government cannot retalitate against you for your refusal to talk.
Generally, in order to talk to you, the investigator would need either a signed Garrity Statement or a Signed Kalkines Statement. The former is a statement saying that they are investigating a wrong doing but you cannot lose your job if you refuse to speak to the investigators, where as Kalkines says you must talk but you are granted immunity for your part in the wrong doing, so long as you make truthful statements.
For more on this, check this legal blog.
There is also the matter that a false accusation (and let me be clear... this is academic, I'm not saying the accusation in the real life topic is false, nor am I saying that the defense is false... we're merely discussing a possibility) is made to your employer and they do not offer the job on the basis of the accusation alone, this is grounds for defamation actions... and in certain jurisdictions, it's criminal defamation, so there could be jail time.
It's interesting you mentioned teachers, because this happens alot. Kids do know that there are certain things that get a teacher fired quickly, so teachers do get the occasional false accusation of sexual assault (I know one teacher who has had multiple accusations over the course of her career). One of the few good things I can say about the Teachers Union is they cover the legal defense of accused teachers. The accusations do get the teacher removed from the class for sometime, but they don't lose their jobs over this matter. It's followed up but the accusation doesn't immediately lead to the teacher getting fired..