If you believe that Swords is wrong on logistics, then provide evidence to support your ideas.
However, you are wrong.
If the French logistic system didn't work, why did they not run out of ammunition? Resupply of ammunition is also part of logistics and the French ammunition resupply system was excellent, as has been pointed out in the past.
And if you wish to actually talk about logistics, then you have to compare the logistic systems of all the major belligerents. The only one that was superior to the French was Wellington's in Spain. However, the caveat to that was that he had to supply a relatively small army and when the supply system did fail, the British troops also went hungry and a campaign could fall apart. Contrary to that, the French would and did march hungry if necessary.