Vernon was worried when Chloe started crying. He requested those words to be embossed in the silver urn as a reminder that Judith didn't die in vain.
She died protecting her grandsons, and Mackie also told him that sometimes her Mommy would cry alone in her room as she was thinking about Judith.
So Vernon knew that Chloe respected her mother a lot, and he thought that giving her the title of an independent woman wasn't wrong.
After all, despite all her problems with Chloe in her later years, Judith was still successful enough to raise two daughters without any help. Vernon also knew that his Big sis Chloe never asked for anything when she was still dating Vincent.
