I was thinking long the lines of what Clagmonster says, the shortest route from Bradford YK Stations is from Interchange. I really am not sure about the logic of a £1.20 Anytime Single having nearly the same benefit as a £5.90 Bradford-Leeds Anytime Return.
FasTIS does say it is valid though, so I looked for another example, Manchester Victoria to City Thameslink and Fastis said it was valid on a Manchester Stns to London Terminals ticket via Salford Crescent and Sheffield to St Pancras and by bus to Blackfriars before walking to City. Now, I assume the planner in Fastis is thinking this doesn't use FCC 'through' Farringdon LUL because it is a bus service rather than the Thameslink or Underground service.
So this got me thinking, what about Cannon Street to Shoeburyness on a London Terminals ticket and Fastis came up with going to Greenwich and taking the DLR to Stratford and proceeding from there.
Southend Victoria to Shoeburyness (Southend Stns-SRY Single £2.10) also comes out as valid via Romford (SOV-RMF Single £8.70)
I think there has to be a bug in the system somewhere, because this doesn't seem right to me.
There is definately something fishy here. My perspective is that in the original example, a Bradford to New Pudsey ticket would only be valid from Interchange and not Forster Square. In some of the later examples, again, they seem wrong and I think there is an error with the planning software - which wouldn't be uncommon.
As regards London - is there not a rule regarding London Terminals tickets and where they are valid to from each general direction? There was also something published (but I now can't find it) about where tickets to London Terminals were valid as far as on the East London Line from the North and South, i.e. you couldn't cross London via the ELL using one.
Another one where NRES is quite clearly wrong is Warrington. Apparently a you can travel from Warrington Bank Quay to Liverpool via Earlestown, then to Widnes using a Warrington Stations to Widnes ticket at £3.10. A single from Warrington to Liverpool alone is £4.30. Again, in this case I would suggest that the only valid route is Warrington Central to Widnes direct.
Apparently a Wigan Stations to Bolton to single ticket (priced £3.00) is valid to travel from Wigan North Western to Preston then from Preston to Bolton, despite a regular direct service from Wigan Wallgate to Bolton direct. Again, this is quite clearly bonkers as Wigan Stations to Chorley is £9.40 and Preston £6.50, so I don't know how it can be argued that the £3.00 ticket to Bolton is valid via PRE & CRL.
Also, back to the OP, according to NRES a £1.10 Single from Bradford Stations to Frizinghall (first stop out of BDQ) is valid to go from BDI - LDS - SHY - FZH. Again, this is quite clearly wrong.
There is definately an error in the system which does the planning here.
Admittedly the system doesn't give these options automatically, it always advises you to walk from BDI to BDQ or vice versa, or from WGN to WGW - you have to force the planner to give you these options. Yet another example of the shoddy back office system used by ATOC for these programmes.
EDIT - Just checked The East Coast journey planning software and that, as usual, is more accurate and advises that most of the journey options advised above are NOT valid. So yet again we have differing opinions with ATOCs own website, yet again, seemingly giving duff (in my view) information.