Water Tank Riddle

Question: Look at the below picture very carefully.

If I will open a tap above tank A, Which tank is the first one to be filled completely?

Answer: Provided the bore of all pipes is sufficiently large to allow a flow greater than the flow out of the tap, no matter how many tanks there are, the lowest tank in the system will always be the first tank to fill.

The inlets to some tanks are blocked so they will never fill. Therefore tank F will be the first and only tank to fill. The verbal explanation given adds that if the pressure of the water coming out of the tap is high, then Tank A will be the first to fill.

That is scientifically incorrect as the pressure has nothing to do with it. All that matters is the rate of flow. If the flow out of the tap is greater than the flow out of tank A, then tank A could possibly be the first to fill.