Yes, correct - and that's still no guarantee that you'll make the flight, particularly if it leaves from a B or C gate (we don't know in this case), if you do that scan at T-36 and can proceed to security. Departure gates close at T-20, so even for a departure from the low A gates, say on a domestic, you'd be partially relying on no secondary check at North security and a clear path to the gate (i.e. not too many people getting in your way). A leisurely stroll through the terminal it's not going to be, and I suspect if the OP wasn't aware of the conformance requirements then they're possibly not in T5 enough to know their way around without thinking.

If you're at a B gate, and certainly a C gate, the chances of making it are 50/50. The benefit to the gate agents once you scan your boarding pass is that at least they know you are on your way, and they can make a judgment call as to how long to keep the gate open before the aircraft misses its slot. If they don't have that information then the despatchers will want to start the offloading process as soon as possible to minimise the delay - which is likely what happened here.