When you ask for permission, you ask your counterparty to consider all possible negative outcomes of the situation, including the ones she is not aware of. In many cases her incentive for the course of action you propose is lower than yours. Therefore, the risk/reward comparison that she makes will often be against the proposed course of action. The result far too often is indecision, and respective inaction, which can be bad for you.
If you, however, take the responsibility for the decision and act without permission, you have two categories of outcomes - positive (or neutral too), where it does not matter you did not get permission, and negative. In the negative case, unless you have violated some ethical, legal, or policy standard, you are still going to have an easier discussion, as you would have to defend your judgment only with respect to the actual outcome of the situation. If you were smart and responsible making your choices, you should be in a defensible situation.