Exchange of experience does mean people. However, it does not necessarily mean - as you seem to assume it does - whole units or large numbers of personnel. As a former military liaison team member I penned many agreements with other nations' military to "exchange information" (or experience) by having them send observers, which I think is far more likely than what the OP seems to fear, to take part in or just watch US exercises and operations.
The alternative, i.e. Russia sending whole military or police units to run security in any significant numbers is both impractical (language barriers, unfamiliarity with U.S. law, public displeasure), very costly and frankly makes no sense.
In the case of the Poles, I not only think it is a good idea that we train together but an essential thing since we have been fighting side-by-side as part of the Afghanistan military coalition the US put together. Much of that fighting was in cities and against drug lords and their operations. The Polish training (and probably lots of other partners' training) has and should be going on.
I am not saying don't pay attention or don't write to DoD or your Congressman asking for good oversight and clear explanations of purpose, cost, etc. But please don't jump to conclusions not supported by or even completely contrdicted by evidence.
I think this administration has made it very clear that the words on the paper are only there as a justification for what they are thinking. Meaning they can twist it to justify whatever they want to do.