For each of those weapons is a Staff NCO who knows by serial number exactly where it is.
For every round of ammunition there is a Staff NCO who knows by lot number and count where every round is.
The “Magnificent Millie” trained officer corps may well be as incompetent and ignorant as the article and the Undersecretary claim, but there is a professional soldier that knows.
However, it is within the realm of possibility that some of the weapons and ammunition are not exactly in the Army’s inventory system. IYKWIMAITYD.
I cannot speak for the Army but the Navy and Marine Corps has a record of every firearm and its location. The list of firearms is kept in Crane Indiana (the Naval Surface Warfare Center, Crane). You have 48 hours to report to "Crane" when a weapon goes missing.
In the 1980s I was the Midshipman at the Naval Academy responsible for compiling the master report to be submitted to Crane. The weapons were M-1s. The rifles were serviceable (only the firing pins had been removed), but had stopped being front line weapons for over 20 years. At the end of one semester two rifles came up missing. They were found in about 12 hours. The rifles had been stored months earlier in a company office, because the midshipmen had left early.
I also remember that after Desert Storm a lot of captured weapons came back to the US and the Marine Corps was having a devil of a time compiling a master list for Crane.