So what is the disadvantage, if any, of having the AVR show PCM instead of Dolby Digital? Any explanation would be appreciated in simple terms.
How much of a purist are you?
The fact that the TV4 outputs multichannel audio as PCM or in a "pseudo" Dolby bitstream is not the main issue here. Most of us are more concerned by the fact that the TV4 is decoding the Dolby input bitstreams in the first place rather than passing the audio to downstream devices for decoding and post processing. The quality of the individual audio channels is probably not degraded per se, however, the Dolby bitstreams carry more than just audio information. For instance, dialog normalization, dynamic range control, and active ProLogic II ancillary parameters tell the decoding device how to post-process audio content after decoding. By prematurely decoding these streams, the TV4 is, in effect, stripping the ancillary parameters from the signal stream and preventing the Dolby audio from being played as originally intended.
As you may or may not be aware, a number of users have complained vehemently regarding the TV4's processing workflow and have gone so far as to return their units and revert to the use of TV2/TV3 devices. I myself have kept one unit connected in the hope that Apple will correct matters by adding a dedicated "Dolby Passthrough" option to the current list of "Auto", "Dolby Surround", and "Stereo" Surround Sound options. Luckily, the DialNorm and DRC issues do not seem to affect my library to any major degree since I encoded the content myself. However, I do have a lot of older AC-3 1.0 (center channel) and AC-3 2.0 active matrix ProLogic II files encoded for 3-channel front (left, center, and right channel) and quad (3-channel front + surround rear) playback. Prior to the release of tvOS v9.1, the AC-3 audio bitstream was passed directly to my AVR for decoding and played as originally encoded. Since the release of tvOS v9.1, such audio content is now decoded by the TV4 and passed to my AVR as 2.0 PCM audio which means my center channel audio now plays as mono/mono (Left/Right) audio and my ProLogic II files play as stereo (Left/Right) audio. Sure, I can apply passive PL II enhancement manually on my receiver, but then I am forced to choose from a list of a half dozen or so effects settings. Further, if I try to play a 2.1 Dolby LogicPro II file, then it is passed to my AVR in a 5.1 Dolby bitstream with unused channels empty. And, since the receiver sees this audio as 5.1 multichannel, it will not post process and play matrix encoded center or rear surround channels. In short, the TV4's decoding workflow simply does not "fully" support Dolby content as it should and as my receiver already does in the correct manner. Unfortunately, since the TV4 functions as it is currently programmed to work, the Apple Developer Team does not seem to consider these failings or inconsistencies to be issues that need to be corrected.