If you MFU a BA-only ticket, the ticket remains subject to the conditions of the underlying cash fare. There are the following additional conditions:-

• Changes to the date or time of an Upgrade flight must be made at least 24 hours prior to the scheduled departure of the relevant flight.
• Where changes are made to the date and time of an Upgrade 24 hours or more before the scheduled departure of the first flight in the Award travel itinerary and the redemption class for the Upgrade is not available on the amended flight(s) the standard redemption charge will be levied for the re–crediting of Mileage to the Member’s account.
• Where changes are made to the date and time of the Upgrade within 24 hours of the scheduled departure of the first flight in the Award travel itinerary or after the scheduled departure of the first flight in the Award travel itinerary and the redemption class for the Upgrade is not available for the amended flight(s) Mileage will not be re-credited to the Member’s account.

The underlying flexibility should remain even after you've made a change, if all you've done is to change the date and time of the flight. If you've changed the cash ticket to another fare category (eg upgraded with cash to a non-flexible fare in a higher cabin and then MFUd that), of course the new fare may have different flexibility rules.

A pure award ticket works differently: that's generally flexible until 24 hours before travel.

So what BA is asking for appears consistent with the way that MFUs work. But obviously, none of us now know what you were shown during the booking process, nor whether you were misled by a ba.com glitch.