It may be an "urban myth" ("urban legend" here west of the pond) in the UK, but I can tell you with authority that it used to be a common practice here in the US.
Not only are there scores (if not hundreds) of cases documented in public sources (with specifics of name, dates, etc), but while working a temporary assignment as a clerk in the ID card/pass issuance office of the base headquarters squadron of Marine Corps Air Station El Toro, California from Dec. 1985 through June 1986, I saw the paperwork many times when retirees or their dependents came through to renew their ID cards or verify continued eligibility for benefits.
The practice was to retire senior officers (Lt. Colonel/Commander and up) concurrent with a promotion to the next-higher rank (effective the day of retirement, and revocable if said officer applied for reinstatement to active duty).
This practice ended sometime after the end of the Korean War, and is currently prohibited by regulation.
Was this the normal practice? No, less than half of retirees received this "perk", but the paperwork I saw & handled was common enough that it was not what I would call abnormal either.
Additionally, many senior enlisted in WW1 & WW2 who received "field promotion" to officer rank, and whose promotion was later not made permanent, reverted to their former enlisted rank... but if they qualified for retirement, they were normally retired "at the highest rank held while on active duty".
This way, there were those who were enlisted men on the date of their retirement, but who were officers on the retired list.