Seems like a reasonable treatment to me.
Most amputations do not bleed because of TXa2 vasoconstriction and formation of primary clot.
However, if you was that clot away with fluid, there is going to be bleeding.
If you dislodge the primary clot moving a patient around, the next one will not have as strong of txa2 reaction or the stability of the initial clot.
You also have to take into account the usage of clotting factors and what kind of fluid you are giving that can affect them one way or another.
A pneumatic TK is certainly appropriate.
It can help to stabilize the clot even further by reducing proximal circulation and pressure.
In the popliteal region, in addition the the named artery, there is considerable collateral arterial circulation. (otherwise your distal leg would go numb everytime you bent your knee)
If it never starts rebleeding, great.
If it does, you are prepared in adavance.
Besides, you can leave a tk in place for relatively 6 hours in many cases and more than one famous patient has died trying to save a limb where in the case of the everyday Joe, saving the life would have been the treatment of choice.