That's either a slight exaggeration or an impressive feat
Having ordered Uber during the taxi, it was already waiting for me, so in within 2 minutes of getting off the gate. 5-7 minute drive to home in Hale Barns.
Best I did was 93 seconds from leaving taxi to gate 141, rare to take longer then 5 minutes. Once the taxi didn't arrive and I had to hail one, got in 10 minutes before scheduled departure time and was sat on the plane (in 1C) before scheduled departure time.
BA have changed since then (there's now a business class section so you don't get to choose 1C), and Manchester Airport is very hostile to people arriving/departing via taxi so I suspect it would take 5 minutes longer now.