The Nationals are the Expos, moved to another city and dressed up in new jerseys. The Nationals can no more claim to be the Senators than an Catholic Irishman who moves to Beacon Hill in Boston can claim to be an elite WASP because Boston Brahmins once lived where he does now.
It's a matter of the keeping of history, which a team located in a market with a century of professional baseball history can choose to associated with and celebrate. It's just like the choice made to have the Ravens not be the guardian of Cleveland's NFL history.
I can understand the franchise itself acting as a conduit to honor how players at a major league venue in realtime. However, I think it more appropriate for that history to have its locus in Montreal amongst the fanbase where it was made. I seem to remember things like that occurring at their hockey arena, with banners and so forth.
Again, we are talking about a century of baseball history here. It is understandable and logical that the custodians of the area's baseball history -- which includes talking about who's hit the most homers ina Washington uniform, who's won the most games in a Washington uniform, and so forth -- would not only make that connection but talk about it more than a nnection to things that happened in another market (and actually in a another country).