Num 20:12: Moses didn't believe in The LORD?

In Numbers 20 we learn of Miriam's death (20:1) and Israel's subsequent contention with Moses and Aaron about the barrenness of the wilderness (20:3-5).  The people specifically focus on the lack of fruit and water in the wilderness.  God responds with some clear instructions for Moses and Aaron for providing water.  Don't miss the verbal details here.  First, Moses is to take the staff and gather the congregation.  After that he is to "speak to the rock IN THEIR EYES"(20:8).  It seems important that the water should be provided through Moses' speaking to the rock "in their eyes".  God wants the people to see Moses speak to the rock.  Instead Moses strikes the rock after asking a revealing question in verse 9: "Are we able to bring forth water for you all from this rock?"  Could this be an attempt by Moses and Aaron to undermine God's role in providing the water?  Could this be an attempt to highlight the ability of Moses and Aaron to provide for the people instead of trusting God to do it by following his instructions exactly?  I think that would explain why the LORD complains that they did not believe in Him, nor did they treat Him as holy IN THE EYES of the people of Israel. (20:12)  Notice the textual link here with God's instructions in verse 8 ("IN THEIR EYES").   So God is indicting Moses and Aaron for not following the instructions properly, and that is why he is displeased with Moses and Aaron.  Here again we see that careful attention to the way the text refers back to other parts of the text through verbal connections is key for interpretation, and this allows the author to guide his reader with his very words.