Which doesn’t really explain much other than that the individual partners have legal jurisdiction over the modules they’ve provided, and (while not clearly stated, the crew has common access to all modules and their functionality regardless of nationality) but the commitments to maintain or retire the elements are unclear. This is problematic if a major player–like Russia or the United States, which owns operationally critical modules which provide environment control, life support, communications, propulsion, et cetera–then the station as a system may no longer be fully functional or inhabitable, thus rendering it useless (or rather, more useless than it already is). Think of the ISS as like being part of a coop housing arrangement in which everybody has do certain chores for which they only have the critical skills or tools. If one party walks away, the dishes don’t get washed, the linens don’t get laundered, or the trash doesn’t get taken out.
This is further complicated by the fact that the US purchased at least two of the initial modules from Russia as part of a cost-sharing agreement and (presumably) maintains nominal ownership. However, there is no guarantee in place ensuring that Russia provide transportation, only an easement to access the station, for which the US currently has no domestic capability. Sucks to be us that we can’t play with our own toys, but frankly, that isn’t anyone else’s problem.
SpaceX can deliver cargo to the ISS. It is not certified to provide orbit raising or transport personnel, nor has SpaceX yet demonstrated a commercial crew capability (though they are working toward this capability and have performed on several significant milestones). They will probably not be certified to carry NASA personnel to the ISS in the next three years even if they had a working system to start certification today. NASA is currently focusing a lot of effort on the SLS and plans for a 2017 or 2018 initial operational capability, but things are not going well there, either.
The Spaceship Company (TSG), the wholly-owned subsidiary of Virgin Galactic, is building the SpaceShipTwo air-launched hybrid rocket engine-powered vehicles for suborbital launch (just barely exceeding the Karman line at ~100 km AMSL) and the LauncherOne for smallsat delivery to LEO, both of which are lofted by the WhiteNightTwo carrier aircraft. Neither of these systems is remotely capable of intercepting or docking with the ISS, much less delivering payload or passengers. The ISS would also make a shitty “fixer-uper”; the costs of maintaining the station are exhorbiant, and because various modules were produced by a number of different nations with limited coordination getting future support for maintenance and refurbishment may be very difficult. The station itself is built with 'Eighties-era technology, and it would likely be cheaper to develop a new station using inflatable modular sections for habitats akin to the TransHab or Bigelow EAM.
Frankly, losing access to the ISS may be a blessing in disguise, especially given the very modest amount of useful scientific research or technology development currently coming from ISS operations. A considerable amount of NASA budget is dedicated to supporting ISS operations, transportation from and to, and of course getting the SLS off in sufficient time for crew transportation despite some of the fundamental problems that ill-concieved program is having getting existing hardware qualified to the new configuration with minimal contractor support. Taking the ISS out of the picture, along with the immediate emphasis on crewed transportation, would allow for more long-term planning based upon developing a sustainable and evolutionary development of technologies for both crewed and uncrewed capability.
This isn’t remotely feasible for a vast number of reasons, starting with the fact that the launch facilities for the STS (“Shuttle”) have already been modified to suport the SLS.