Sorry I haven't been too involved in this, as qwerty and Godspell seem to be able to help quite well. But I couldn't let this one go so simply.

Perhaps you should read a little further in Mathew to find:
Matthew 8:2-3 2 A man with leprosy came and knelt before him and said, "Lord, if you are willing, you can make me clean." 3 Jesus reached out his hand and touched the man. "I am willing," he said. "Be clean!" Immediately he was cured of his leprosy. (emphasis mine)

or a little later still:
Matthew 8:24-26 24 Without warning, a furious storm came up on the lake, so that the waves swept over the boat. But Jesus was sleeping. 25 The disciples went and woke him, saying, "Lord, save us! We're going to drown!" 26 He replied, "You of little faith, why are you so afraid?" Then he got up and rebuked the winds and the waves, and it was completely calm. where here Jesus was quite content to let the disciples face the storm themselves, perhaps for their own benefit, knowing that they could handle it even if they did not know it themselves. That may or may not be, but He was certainly exasperated that they were too afraid to abide by His will to let the storm rage.

and perhaps you recognize:
"not my will, but Yours be done"
and
"thy kingdom come, thy will be done, on Earth as it is in Heaven"

It is quite clear to me that Matthew was quite certain of Jesus ability to choose not to heal, not to calm the storm. Sure, in both passages, he does, and in the many other stories I could reference where Jesus seemd content to not heal, not calm storms, but did so for other reasons (usually proof to someone who needed prooving to.)

Matthew 7 is part of a sermon of Jesus' about not being concerned about where our worldly needs will come from and trusting the Lord to provide them. It is a promise of trust, not a formula for "abaracadabara amen." Much of popular Christian theology around prayer is based on this pagan-like way of thinking; that we can force our will on God through legalistic interpretations of His promises to us, by taking them out of their rightful context and twisting them to serve our wants.

It doesn't work that way, hun.

God is Soverign. Think Aslan from my namesake's "Chronicles of Narnia": The Great Lion is not safe, but He is good.

There is nothing tame about our God of Fire and Storms, nothing controllable in our God of Life and Death, nothing easy-going about our God Mercy and Wrath. But He is good. He is the God of Love, forgiveness, compassion, who died that we, His children, might live. He loves us, and will do (as He has actually promised!) what is best for us as his rightful wayward heirs, despite our begging and screaming and crying to be other than He wills.

If He chooses to 'heal' me, I shall be healed, and I will be glad of it.
If He chooses no to, then I shall not be healed. And I will try to be glad in that too, since that seems to be His choice.

"Not my will, my Lord and my God, but Yours be ever done in my life."
Love in Christ,
~CSL