There is a difference between 'is it safe' and 'is it compliant'. Nothing is 100% safe, things are only ever 'safe enough' to allow reasonable use. Gas appliances such as your fireplace are required to be tested prior to being sold so that the standards of safety that society expects are maintained. In this case the manufacturer would have had a sample unit installed in a laboratory and tested against the relevant safety standards (the fire burns efficiently enough, it doesn't leak smoke and exhaust into the room and it doesn't make touchable surfaces too hot etc). Once it passes the tests, the manufacturer gets a certificate that says this unit is safe to sell to the Australian public. Now that test certificate corresponds to a particular configuration of the unit and its installation - if the configuration is different, they need a separate test to cover that different configuration.

So since your unit does not have a trim frame it would not be identical to the model tested and therefore would not comply - unless of course the manufacturer also tested it without the trim. So this is the question you need to get them to confirm.

In all likelihood it is probably 'safe enough' without the trim, but if it is 'non-compliant' you risk an insurance claim being rejected (if say the fireplace caused the TV to fall off the wall somehow lets say).

At the end of the day if you leave it without the trim frame, try and get a letter from the manufacturer and the installer stating that your particular configuration complies