You are correct that in the Hhonors terms and conditions, it states the eligibility criteria:
Eligibility for all on-property HHonors benefits, including complimentary Internet and MyWay benefits such as complimentary snacks and beverages, complimentary continental breakfast and space-available upgrades, requires a confirmed reservation made through one of the following channels:

Any official direct Hilton Worldwide hotel brand or HHonors website (for example, HHonors.com, Hilton.com, Hampton.com, etc.),
Hilton Reservations & Customer Care phone line (1-800-HHonors or local Hilton reservations office),
Hilton HHonors or Hilton mobile application,
Directly at a hotel in the Hilton Worldwide portfolio, or
Through an IATA accredited retail travel agent professional ("Travel Agent") booking through a Hilton Worldwide channel or the following Global Distribution Systems: Amadeus, Apollo/Galileo, Worldspan and SABRE.
On-property benefits are not awarded in the following circumstances:
Reservations booked through a non-Hilton Worldwide-direct booking channel or a non-designated GDS, third party website or any other channel,
Rates available on "opaque" websites where the hotel brand and specific hotel are not known until the booking is made, or
Third party hotel packages or travel packages not booked through one of the eligible channels.


So if your reservation is through one of the approved GDS systems, you should receive the diamond benefits. Unless any other Flyertalk members can tell you whether ba.com uses these systems, perhaps you could enquire through British Airways?