Sean- To give you a different perspective, the amount of pressure that you can put on a fish with your rod depends on several things besides tippet strength, some of which include:
The action of the rod. A fast and heavy rod will exert more pressure than a slow rod.
The angle of pressure. Side pressure can usually exert more, and anything that is vertically greater than 45 degrees usually results in less pressure.
Drag of flyline. If a fish is 50 feet out and is dragging about 40 feet of flyline around with it, this contributes to the pressure. The heavier the line, the greater the pressure.
There are more, but these are what really stand out for me. Taking these into account, I think it's reasonable to assume that a flyrod of the right type and correct rod angle during the fight can result in far more than 6 pounds of pressure.