I know all of the above is true. One of the "great advantages" of membership of the EU is this type of reciprocal agreement.
However, in view of the wide disparity between level of benefits payable in the two countries, it has to be asked what is in it for the hard-pressed British taxpayer. After all, he's hardly likley to up sticks and live in a one-bedroomed flat in Warsaw just to claim his means tested 10 Zlotys a week is he?
A fundamental problem with these "great advantages" is that whilst, on paper they are reciprocal, in practice, because of the disparity in the economies, they are effectively unilateral.