Thank you! I remember the Vanity Fair article, but its incorrect suggestion that an HRH title is a peerage does not provide a basis to infer whether it was an HRH title or merely a peerage which was offered from the queen. (For newer readers, a peerage is a title of duke, marquess, earl, viscount, or baron/lord.)
The actual quotation from the Princess Royal states only "titles" and is not precise about whether the titles were royal titles or peerage titles.
The Tatler article also does not precise whether the titles offered to Princess Anne's husband and children were HRH titles, or titles from the peerage.
At the time Princess Anne gave birth to her first child, the media coverage suggested that the titles she was offered for her husband and children were merely peerage titles, rather than HRH Prince/ss titles.
https://www.nytimes.com/1977/11/16/...irth-to-boy-fifth-in-line-to-the-british.html
In a departure from tradition, the child will not be given a title. [...] No reason was given but it was speculated that the young parents, both of whom are known as freewheeling and independent, did not want peerages for themselves or their children.
BBC ON THIS DAY | 15 | 1977: Princess Anne gives birth to Master Phillips
Both the princess and her husband are said to have rejected an offer from the Queen of titles which would have enabled their children to be born into the peerage.