Writing on a whiteboard is not defacing property unless they didn't use the correct markers and stained the board. It seems like there is something more to it than that.
If HR/PR lied about defacing property it would open them up to a defamation lawsuit. The entire purpose of HR is to protect the company from lawsuits which is why they don't usually make up fake reasons for firing people. They just won't give specifics instead of defaming a person publicly.
"Defacing property" doesn't have as strict a definition as you think it does, as an example: https://codelibrary.amlegal.com/codes/morrisonco/latest/morr... <- Writing on a whiteboard wall would qualify under that definition even if it's not what you think it is.
The fact that it comes from Google directly should make you more suspicious not less.