It's a common mistake, and one that's caused many an argument on a softball field: Sometimes, you can't read just one tiny snipet of the rule book from a single rule and assume it applies equally in all situations. Quite often there will be another rule that makes an exception to or conflicts with the other rule. You really have to take the rule book into account as a whole, not as a collection of dozens of unrelated rules.
Why is there an exception to this rule? A couple of reasons.
First, the play you describe does not really meet the definition of interference. Maybe this defensive player was "confused", which is part of the definition. But the "confusion" did not prevent the defense from "making a play", which is another part of the definition that you are overlooking.
This is another case where you need to read more than one little snipet of the rule book to fully understand the ruling. There is a definition for what "making a play" means! "A play" is an attempt by a defensive player to retire an offensive player (ie: an attempt to record an out).
On your play, the batter was already out. A throw to first base cannot possibly "retire her again". The throw to first base was not part of an attempt to record an out, because there was no out to be gained there. Thus, a play was not interfered with and it's not interference.
As for the other two runners, the batter didn't prevent the catcher from throwing the ball to second or third. Those options were still there and the catcher could have made those plays unimpeded. The catcher's ignorance of the rule and unecessary throw are on her and you don't penalize the offensive team for that.
I believe that the exception is in there just to clarify a play that is fairly common in fastpitch. Batters are usually coached to start running to first on any third strike that isn't cleanly caught, even when not entitled to advance. This being interference or not was such a commonly debated point that the exception was added to clarify that it is not.