Regardless of the genealogy, I think Frances was trying to point out there are no authentic Manx Arms.

A Coat of Arms is granted to an individual by one of the Colleges of Arms - England, Ireland and Scotland. The subsequent use of the Arms may be inheritable, usually by the senior male line, but there are exceptions.

There was not, and there is not, any Body on the Island that granted Arms.

The fact fhat someone, somewhere with the same surname has a Coat of Arms in no way confers the right of usage on any other person with the same name.