The Persians in their heyday had a great ability for putting together large armies and supporting their movements. The foolish "must have been exaggerated by adding a zero" nonsense is, uh, foolish nonsense.
They bridged the Bosphorus at least twice (once during their attempt at conquering the rest of Greece, another time when they marched around and tried to corner and control the Scythians) and during the latter also bridged the Danube.
As in all successful ancient empires, on a fresh venture they used a massive force to overwhelm their enemy, and set up local governance. In the two examples above, they did neither. :^)
I've wondered why the Persians didn't use ships to move their forces to a point along the coast and cut the marching distance to Siwa to about 40% of overland route from the Nile. Logistical support would have been much simpler as well. Cambyses had used naval forces in his conquest of Egypt, but the Persians never seem to have developed a permanent navy, hiring ships from among conquered peoples seems to have been their expedient.
The later Roman Empire famously recovered a beached Carthaginian vessel and copied it in the hundreds, then equipped their vessels with special gangplanks, turning their sea battles into land battles. Not until Augustus did the Romans establish a permanent navy, building at least five major naval bases and obliterating piracy.
One thing that's worth considering is that the Persians were used to deserts, being hemmed in to an extent, and also had a well-trained, experienced, disciplined standing army.
Damn, you know a lot!
There was also a ton of booty between points A and B by land.