Air Carrier crew was questioned by ATC after an 'amended' altitude was issued shortly after a crossing altitude instruction was given. The flight crew was descending according to the original clearance.

Narrative

Prior to EED at FL380; we were given; 'Descend and maintain FL360; cross EED at FL300.' During our descent we were given; 'Amend altitude FL340.' Then we were handed over to a new ATC frequency. I checked in with the new sector with; 'FL340 cross EED at FL300.' At FL302 over EED; ATC asked to; 'Verify altitude 340?' We stated; 'We were given EED at FL300.' No further dialog was exchanged. While preparing for our return flight; Dispatch called to inform us that we needed to call the ATC facility. We understood the amended altitude to be the new initial required altitude and that the 'cross EED at FL300' was also still required. The ATC Manager stated on the phone that there was no separation or conflict issue with other aircraft. Looking back; it felt like we may have been 'lost in the shuffle' between controllers. We were under the impression that we were doing as required. The ATC Manager stated that when the amended altitude was given; that was now our limit to descend. When I checked in with the new frequency; I even stated that we were crossing EED at FL300 and he said nothing to contradict my statement. If we were wrong in our understanding; I would have thought the new Controller would have said something.