There are quite strict rules on waving a warrant card about off duty unless there is genuine operational neccessity to do so, eg, an off duty arrest, etc. People have been sacked for flashing their warrant card at road users and the like even when they were, technically, correct in what they were saying and weren't gobbing off or being threatening. I'd suggest the story is likely apocryphal.
Operational policing necessity is the test for justification. If it can wait until the officer is back on duty, or can be resolved by calling 101/999 then they should do so.
The only times I let mine loose when not at work was when claiming free rail travel, which was authirised, and ata motorway services - the lad on the till saw it in my wallet (I never used the sheety issue warrant card holders) and asked if I was a copper. I said yes, and he said "oh, 20% reduction for you guy" (again, an authorised diacount arranged via the local Federation, encourages coppers to pop in for lunch while on duty), and asked to see the card so he could note the details for the till log.
If I encountered any officers junior to myself (I retired as a DS, but had my Inspectors exam and had temped at that rank for a few months before deciding it was the sheety end of a stick, a slight drop in salary for a lot of grief) acting like bellends when then it would be a call to 101 to report it to the duty Inspector, as we were all told to do.
All the years and years and hundreds of thousands of pounds of specialist training isn't teaching you how to be a copper. No, its teaching you how not to stitch youself up!
