“We have no evidence” strongly implies some sort of extensive forensic dance was performed, and was fruitless. “We have no way of knowing” sounds much more like epistemological resignation. “Evidence” is a pretty loaded word to use.
"We have no way of knowing" may not be correct statement. There could always be a way to know that you may have missed. It would be inhuman to claim "we have no way of knowing" in circumstances like this.
Fair enough, perhaps to be more specific they could say "we have not kept sufficiently detailed logs to determine what happened"