Typically on trees branches that extend outward from the trunk at a horizontal angle are strong branches. Vase like shapes (like those in my least favorite tree the Bradford pear) tend to have weak branches since the branches are exerting more force where they join up with the trunk. They also peel away large pieces of bark along the trunk when they get damaged in storms.
Just wait until you see the way the tree looks now.

I understand why the tree was a concern. It was planted very close to the house and had large limbs that extended over the roof. The fear of a large branch coming through the house is definitely no laughing matter, but think of what happens now. The new branches are significantly weaker than the ones that were on the tree for the last 20 years and will eventually grow over the house. If diseases, insects, and rot don't fester in the wounds of the tree and it survives long enough those branches will again be a concern. Then it will need to be pruned again, oh wait this wasn't pruning. Pruning is what should have happened. A licensed arborist should have been hired to determine what branches should be taken out. The arborist would not have pruned out more than 1/3 of the branches at any one time and it would not have resulted in the stubby giant oak that you see in the picture. If you need an arborist to take a look at your trees please call your local county extension agency, they are there to help you...use them!
The other option would be to remove the tree completely and plant a new smaller tree in its place. One that wouldn't extend branches over the roof of the house or pose any threat of damage. A redbud might have been a great one to place there. This is why it is so important to plant trees in the right spot. You may not be concerned with it today when it's an elegant little sapling but when it becomes a graceful giant you will be!