Not quite. Basically, Dolby Digital, TrueHD, DTS HD etc. are all just ways of compressing a soundtrack. The older Dolby Digital and standard DTS used more compression than the new formats like TrueHD because there wasn't so much room on a DVD as there is on a Blu-Ray. However, even with all the space on a Blu-Ray, some compression is still needed in most cases, hence these newer formats.
When an amplifier with the appopriate decoding chips receives a Dolby Digital signal, it decodes this signal to a PCM format which can then be used to send sound to the speakers. Because an amp receives the Dolby Digital signal, it knows what format it's in, so most manufacturers get their amps to display "Dolby Digital" on their displays telling the person this is the format. In the case of the PS3, what is happening is, for the newer formats like TrueHD, the PS3 is actually decoding the signal to Linear PCM and then sending this to the amp. The amp therefore doesn't have to complete this decoding step, but can just use the information to send sounds to the speakers. Because the amp didn't receive the signal in its compressed form, it doesn't know it was originally Dolby TrueHD, so you won't get anything on your amp displaying this. However, as long as you're getting sound from all your speakers, you can be sure you are getting the correct format.