It's been a little while since I did Air Law but I'll have a go...
IATA does not regulate safety, it's just a trade association. Safety is regulated by the state under the guidance of ICAO.
A safety demonstration is required on a UK registered aircraft. Customer service would be wrong if this was a BA flight. They are
probably wrong about QR aircraft too but I'm not certain.
On a BA aircraft the regulation you'd be looking for is contained in EASA Part-CAT. Specifically "
CAT.OP.MPA.170 Passenger briefing". Page 126 in
this document is a good place to start.
However, on a QR aircraft the Qatar CAA would be the governing body. I don't know their exact requirements however it will be based on
ICAO Annex 6.
I think
fransknorge is right, customer service is not the best avenue to follow with this, although proving them wrong might make you feel better.
