My understanding is that the tax-free status would apply only if your pension is an invaliding pension and you were discharged for the PIC that has attracted the higher War Pension Scheme award.
That was my understanding too, but in most cases it's the MoD having their cake and eating it i.e. you can't apply for a War Pension whilst serving so, unless your injury is quite severe, you won't get a SIP and if you do, as your conditions deteriorate over the years it becomes more difficult to be successfully awarded a deterioration claim whilst your SIP/pension only goes up with CPI.
In my case I didn't know I had to apply for a WP myself (and I was a SNCO) until a number of years after leaving the regulars, in fact I was on FTRS when I found out, but as I was chasing an NRPS post I didn't/couldn't apply. The 50% WP I currently receive only started once I suffered a serious injury* on NRPS that got me medically discharged, I applied for a WP myself and got to that % through adding other documented injuries and deterioration claims (after originally getting awarded 20%) which again I discovered I could do instead of getting advised during the discharge process or via veterans uk.
I do think there's a case for the MoD to consider reviewing the cases of those receiving a Pension & WP and potentially changing their Pension to a SAP, but tbh it could cost them a lot of money and the applicants a lot of heartache/struggle.
To complicate my case further, I was AFPS75 during reg service, FTRS & NRPS, but the way the MoD do the pensions (seperatley instead of rolling them together) means I'm unlikely to ever have my regular pension amended to a SAP.
ETA For clarity
The injury I suffered on NRPS was covered by AFCS, the War Pension I receive covers 11 different injuries.
