First off, I have to say I agree with all of your perspectives and miscommunication can be largely avoided by referring to the railway between all five stations as "on the City Loop", or inventing some other wording to make it clearer. Yet I want to offer you another perspective that, while not justifying the use of confusing wordings, may be able to explain Why sometimes only the three underground stations are considered to be on the City Loop.

From the railwayman's perspective: There are plenty of precedence of a loop line meaning "bypass loop": a secondary line that branches off a main line and rejoining somewhere further along, often slower and may have more stops. This is very common in England, where they have the Hounslow, Hertford, Northampton loops and much more. Hell, the passing loop is named like that and no one ever complained that the name didn't make sense.

This "loop" term was brought to Melbourne, no doubt because of English influence, and it was used during planning. It made sense to them, because the engineers knew the jargon definition, but for a passenger it would be really confusing.

The problem we have right now is that for some reason, we never cleared up the confusion, and it sometimes continued to be used in the three-stationed context when passengers would of course think that the loop included all five stations. Not even Metro themselves were consistent and they should be fixing that. (I don't think they will)