I think some of the confusion is that DLRP has only had two parks for 6 years, so before that people always used to refer to the Magic Kingdom as the Disney park because there wasn't anything else there, so it wasn't confusing. Then when Studio's was born I think it developed the nickname of the Magic Kingdom to make it easier. I refer to the Disney park as either Magic Kingdom or The Main Park when I'm talking to people about it.
The fact that people are calling the Disneyland Park the "main park" probably makes the executives' stomachs churn, because that's exactly what they don't want it to be. (Of course, it's their own fault for building a park that no one in their right mind would equate with the park next door.)
I do think the name contributes to this, though; having a "Disneyland Park" at a "Disneyland Resort" makes it sound like the most important asset, doesn't it? If Walt Disney World had been called the "Magic Kingdom Resort," its first park would seem a lot more important as well. But I digress.
(Hmmm, maybe they picked "Disneyland Park" because it was cheaper — they only had to replace "IS" with "K" on the sign above the Disneyland Hotel entrance this way. Gold leaf is expensive!)
But again, this was not some glitch, the mention of "the Magic Kingdom" at the train station is intentional. It's just a nickname. Like "the Big Apple" or "the Garden State."