Anderson was traded before the deadline. In fact, I think it was announced with the additions.The reason was so that the Marlins could add him to their 40-man roster.
The Twins could try to trade a non-added player. Let's use Jax as the example, and I think you may have answered your own question. Those guys can't be added to the 40-man now, so the acquiring team would then risk them being taken.
It's the same reason that teams generally try to not announce their minor league signings until after the Rule 5, so they don't have to risk losing them. You may recall that one year the Twins signed RA Dickey to a minor league deal, then a week later the Mariners Rule 5d him.
Likewise, a guy like Jax's value does go back up immediately after the Rule 5 draft, if he isn't selected because now the team has a year to determine if they would want to add him... but that is also true for the Twins.
Thanks Seth, that's what I thought.
What is more exciting is that none of Lewis, Rooker, Kirilloff, Larnach, and Balazovic have been around long enough so that they needed to be added this year.Heck, wouldn't surprise me if all of them get added during the season next year because they have played their way onto the team.