On our mixed fleet of 744's, Body Gear Steering works just fine, every time during maintenance tows with all 3 IRU's switched off.
Agreed, but with IRSs off, the IRS LEFT Advisory Message is removed (so the QRH statement is partially true). I even asked Boeing why BGS was still available with the IRUs off. They said it's just the way the logic works.
Our manuals don't seem to have an answer to this (I've been digging for a while).
So what are some of the possible variations?
1) It's an option to have multiple IRU inputs (This might explain the differences between airline QRHs).
2) Only one IRU is true for all aircraft (the other QRHs haven't been updated yet and the engineering books are wrong).
3) The QRH is correct in saying that that you will have no BGS with the Left IRU message in view... but the guy who wrote it forgot to tell you that you can select another IRU to fix the BGS (unconfirmed) or switch off the IRU to fix the problem (confirmed).
I don't know if the BODY GEAR STRG message appears whenever the IRU LEFT message appears (or if the BGS system needs to have a command (on) signal first). The FIM fault logic has a lot of "and" and "or" statements (with commas and full stops in confusing places).