and i'll tell you the lawyers will rip that to shreds.
Further, don't take the word of a watchdog rep. Look to the source document directly.
Here is the contract of carriage from united (from a quick google search).
https://www.united.com/web/en-US/con...-carriage.aspx
Unless I missed it, there is no definition of boarding and a distinction in the document from boarding to one reference to "boarded". There is also no reference to boarding and the doors have closed.
It's possible it's in the US legislation, but it does not appear to be in the contract. United has a pile of rights, but they can't invent new ones that aren't in the contract without facing scrutiny and risk.