Well, he did say, "The
coach should have argued...". You would expect a coach to make a screwy argument like that!
As the coach, what he should have asked is, "In your judgment, do you think the runner would have safely reached third base if she had not been obstructed?".
If the umpire answers, "Yes", then you're pretty much dead in the water. You might put up a mild argument as to why you don't agree with that, but that probably won't go anywhere and you don't want to push it. By declaring that the runner was placed on third due to the umpire's judgment means that the rule was correctly applied (even if the judgment behind it may have been faulty).
If the answer you get is something different...you now have a possible protest in the making. If the umpire tells you he doesn't think the runner would have safely reached third base, then the runner should not be there!
Your next question should be, "Then why did you place her there?". Perhaps he is under the mistaken belief that obstruction carries with it an automatic "forward" base award. That is a misapplication of a playing rule and that is grounds for filing a protest.