In most states polygraphs cannot be used as evidence. Polygraphs can determine if someone is tellingthe truth --or so they say. But false negatives are also very possible. that means a person telling the truth may reguister as lying. The converse is not true.
If you have a lawyer, he will likely tell you to have a private polygraph performed. If it indicates truth, provide that to police. If it does not, it does not have to be dislosed.
They can charge and they can convict on only the victims word. In fact, that is usually how those cases are charged and how they are pursued.
This is my area of specialty. Most of my criminal defense cases involve those exact types of scenarios in Minnesota.
Think of every word that is given as another piece of evidence to be twisted. He should also discuss this with no one.
Presently, the case is weak. They can still charge it but will be reluctant to do so without more. If it is alleged that he is a pedofile, you may see a warrant for his computer to seek evidence of child pornography or correspondence that is inappropriate to children. That warrant can be challenged. yet, I have seen those warrants allowed, at least initially.