This should illustrate the problem quite clearly:
This is the Czech 4th Brigade, with all of its equipment, in parade formation
This is the largest transport plane that the Czech Republic has, and there are 8 of them:
See the problem? US IRF Brigades can deploy to anywhere in the world within 18 hours notice. 82nd Airbourne Division for example, alongside the 101st Airbourne Divison, is capable of this.
Czech Republic, without USAF assistance, would have to haul all their vehicles on trains all the way to the ass end of Eastern Europe, taking days.
It's just not the same capability.