Thank you @Victor Eng and @Andrew Johnson for a helpful and quick response.
It seems like the property was tested twice. For the first time both units were tested during the current sellers due diligence period. He didn't mention that, but maybe he just does not remember since it was in 90s. Then he tested one of the units in early 2000s. He used a different inspector every single time.
When it comes to remediation I believe that there was nothing done at all (except windows change and that was done to not to loose so much heat in the winter). Currently there are not any kids 6 or younger living in the property, but I do not have any idea if there were any in the past.
I checked the list of inspectors in MA (http://www.mass.gov/eohhs/docs/dph/environmental/lead/ma-lead-inspector.pdf) and both of them are still licensed. We actually called to the second one who inspected that one unit in early 2000s prior to this conversation when we were calling three different inspectors to find out pricing and availability. Does it matter in this case if we ask the first or the second one to do the inspection again?