As a diamond dps main who is also a high plat/low diamond lvl support player, I’d rather play Ana or Moira if I had to play against a team of silvers than dps.
Contrary to what a lot of low elo tank/support think, it’s extremely difficult to 1v6 an enemy team even as a dps smurf. You need your team to do SOMETHING to keep some of the attention off yourself. Because otherwise the enemy team will just be watching for you constantly and every time you engage will turn into like a 3v1 or more, which is hard to win even as a smurf.
Whereas with Ana, the focus of the enemy team will almost never be more than just 1 player vs you, if you are playing correctly with your positioning. So the diamond ana just needs to be able to win 1v1 battles, whereas the diamond genji would need to win 3v1 or even 6v1 battles in silver. Especially on attack, when the enemy team can just bunker in and if your team is afraid to press w, there’s really nothing you can do sometimes.
Ana can just build her ult extremely fast and nano her teammate when they ult and wipe them. Genji and McCree are both very limited in what they can do, if they get absolutely no heals, which is probably common for a dps player in silver.
So yeah, your theory is pretty wrong