If the Nationals wanted him, they could have claimed him off waivers. They did not do so.
If a player is waived, any team may claim him. If more than one team claims the player from waivers, the team with the weakest record in the player's league gets preference. If no team in the player's league claims him, the claiming team with the weakest record in the other league gets preference. In the first month of the season, preference is determined using the previous year's standings.
If a team claims a player off waivers and has a viable claim as described above, his current team (the "waiving team") may choose one of the following options:
arrange a trade with the claiming team for that player within two business days of the claim; or
rescind the request and keep the player on its major league roster, effectively canceling the waiver; or
do nothing and allow the claiming team to assume the player's existing contract, pay the waiving team a waiver fee, and place the player on its active major league roster.