"They're not saying these people aren't press, or that they can't publish whatever they want. They're just saying they don't get to enter the building as press."
What is being denied, follows; access to the building is incidental to this:
1) Timely Access to Content and Details
For News time is of the essence. "The early birds get the worms." Old news has no economic value, unless you are writing a history book.
2) Opportunity for Q&A
Different people ask different questions. Less risk with less diverse and limited participants may be a motivating factor. If we suspect that we will not like the questions you ask, we won't let you in to ask them.