(I think) the case depends on what AI watermarks are. As far as I know, things like SynthID has practically zero false positives.
I think you need to provide independent sources for the "SynthID has practically zero false positives". Except a paper written by Google authors about SynthID for images I have not found any study about zero false positives.
My understanding is that you get back a percentage from SynthID regarding how confident it thinks the text is generated by AI or not. The question is what percentage would be considered undeniable that it is AI generated or require more than just your testimony to prove that you actually did the work yourself. https://www.nature.com/articles/s41586-024-08025-4 (Google Deepmind) was using a "Watermark detectability is measured using the true-positive rate (TPR) when the false-positive rate (FPR) is set to 1%" for instance in their research paper. This 1% was set arbitrary just for the research paper but what percentage should it be set to?