Automatic Batter Interference?

[JaysDad]

No outs, right handed batter, right handed catcher, runner on first.

The runner steals on the pitch, the batter swings and looses his balance and stumbles toward the plate. However, it didn't seem that he stepped on the plate. The catcher came up to throw to second, but didn't.

The runner was safe at second and the plate umpire didn't call anything on the batter. The defensive manager came out to ask for an explanation of why the umpire didn't call interference on the batter. The umpire said that he didn't think the batter interfered. The coach wasn't satisfied, but went back to his dugout.

If the batter swings and stumbles toward the plate while a runner is stealing, is it normally considered automatic interference on the batter? It seemed that several people on the defense thought so.

Thanks for your help.