Totally get what you're saying about spurious allegations. If my child was simply accused by one child, and my child said that she didn't do it, and there was no previous indication from my child that she would act in such a way, I'd be in her corner 100%.
Here, though, there is evidence. Independent evidence from the girl's own best friend. Coupled with the fact that the girl has recently been found to be lying about something unrelated, granted, but indicative that she would lie if it benefited her to. And also that her behaviour has been difficult recently.
I could understand if the girl had not lied, been difficult, there were no witnesses etc. But that isn't the case and that one witness is actually her best friend says alot.
It is very rare to have tangible evidence as you previously referenced the absence of. These sorts of things are usually he said she said. Yet here it's actually up a notch from that as there are witnesses one of whom is independent/more likely to be bias in favour of the accused girl.
If this were a court matter, the best friend witness would be very compelling.
If I were in OPs shoes I would be careful not to say I didn't believe my daughter because there is always the chance that she is being truthful and I would not want to damage our relationship in terms of her coming to me with issues in the future. So I agree with you that it isnt right to jump to her being a liar. However I would sit her down, explain the evidence, explain how it doesn't look good, explain how there is to be an investigation and what that means (having found out about the process myself) and that I will support her whatever she did or didn't do in that we will work through it together however she needs to be aware that she will be in a much better position if she is honest now, if she did it, than later. I would explain what the consequence would be if she did it and said so now and what the consequence would likely be if she did it and was instead found to have later (like when you get a reduction for a guilty plea) so that she was fully informed to make a decision. If she continued to deny it I would support her - not actively telling everyone she didn't do it but in terms of supporting her emotionally while trying to be objective about the investigation- and then if the outcome is that it is considered that she did do it I would follow through with the more severe consequence I had previously explained to her.
For me, the consequences would probably be a short break from training to reset versus potentially removing her from the club irrespective of the club's decision so that she appreciates the increased severity of not telling the truth. If she is telling the truth she should have little to worry about and she may be able to suggest to me other people who would've been training at the same time as comments were allegedly made who could speak in her favour given that it sounds like this has happened on a lot of occasions.