there is no such thing as an inertial frame or near-inertial frame that crosses an event horizon.Sure there is. Consider an object falling into the black hole; you can set up a local inertial frame around the event of that object crossing the horizon and it will work just fine even though it straddles the horizon.
What you can't have is a static inertial frame that crosses the horizon; i.e., you can't have one that stays at the same radius, even for an instant. The inertial frame I described above is infalling--i.e., an observer at rest in the frame is falling into the hole.
But there is no near-inertial frame that, from within the frame itself, appears to cross the Rindler horizon.
Yes, there is. This is even easier than the black hole case because you can have a Rindler horizon in flat spacetime, where all inertial frames are global--they cover the entire spacetime, including the region behind the Rindler horizon.
I should note that I do not mean to imply that the "finbot" article linked to is correct; it isn't. As I described above, inertial frames that straddle the horizon can be constructed, and they are perfectly consistent with the equivalence principle.