That doesn’t seem to be true? Their site says you can use another passport as verification if renewing - https://www.gov.uk/renew-adult-passport/renew or if applying you need a little more https://www.gov.uk/apply-first-adult-passport/what-documents-you-need-to-apply
I’m about to have to go through this now. I’m a dual citizen but I’ve never lived over there, and have a trip planned to visit family later this year. I let my British passport expire over 10 years ago because I never use it.
More details here too https://www.gov.uk/government/publications/overseas-passport-supporting-documents-group-3/applying-for-a-passport-from-outside-the-uk-supporting-documents-group-3-accessible The supporting docs in table A are definitely doable without living in the UK, if you even need to use that table. Their site is unclear and contradictory unfortunately between that last link and the earlier ones
They do seem to be good at making a mess of things.