Air carrier Captain missed crossing restriction and altitude assignment; alleging both altitude and airspeed information was relayed to the Controller appropriately.

Narrative

Our last ZDC Controller cleared us to FL250. We were coming up on RIDGY Intersection on the KORRY 3 arrival to LGA. The crossing altitude for RIDGY is FL270; but ATC does take us below and stops us above these altitudes; at times. We both heard the assigned altitude of FL250. When I checked on with ZNY; I gave the Controller our assigned speed of 250 KTS and FL250. I even said 'FL250' with emphasis since it was below the FL270 altitude for RIDGY and we were short of RIDGY. The Controller did not correct our altitude or question it on my check-on. However; shortly after check-on; the Controller asked what our altitude was and I told Controller FL250. The Controller asked who assigned us that altitude; and I said that it was our last ZDC Controller and I reminded the Controller I had checked on with FL250. The Controller said that I had only checked on with my airspeed of 250 KTS. A proper check-in includes altitude and we both know that I did check in with both our assigned speed of 250 KTS and FL250. Many years ago the FAA took responsibility away from Controllers for making sure that pilots give the correct altimeter settings; altitudes; etc.; and made it a pilot responsibility ONLY. That greatly reduces our safety margin and I really do believe that this needs to be a joint responsibility once again! Since the controllers no longer share responsibility; they don't listen to what we say when we check in!