Viva la revolution?
I think that it easy to get the impression from the online 4E audience that core really denotes all resources authorized enough to be part of DDI, at least the character builder. The ease of use of this resource makes it much easier to accept new material, balanced or no, as a "core" part of the 4E experience.
Other choices by WOTC cement this notion: releasing classic races and classes in books other than the first Player's Handbook, adding classic monsters in the same way, and making the DDI resources the most up to date, errata'd versions make it both more appealing and sensible to make use of what is available.
It would be possible to exclude certain resources using DDI tools, but it is easier not to.
Earlier editions of D&D lacked these tools. After a while, "core" becomes an exclusive definition rather than an encompassing one for reasons of ease of use and DM resources rather than anything to do with the balance of the rules themselves. Though I've noticed that 4E has not yet created a new subsystem to replace something that is already there, or as an alternative to it; as an example, the character builder allows both hybrid characters and its traditional feat-based multi-classing, rather than making players choose. In 3E, a DM would really have to decide, with care, whether to use the traditional fighter or its "replacements" in Bo9S, for example.
Without the DDI, though, I think it unlikely that gamers would consider everything core - simply calling the rules "core" or giving books names like "Player's Handbook 2" doesn't make them so, in 4E or 3E. What would be good to know is just what percentage of 4E groups make use of DDI.