That’s an irrational statement. If your statement were correct, companies would always be hiring and never outsource or have layoffs.
Productivity increases are achieved through technology advancements, on going employee training , better tools and procedures plus improved management process and a nearly endless host of other factors.
Note that I said "to first order" (look it up if you don't under what that means) - obviously at some point the diminishing returns sets in and incremental productivity goes to zero. For many enterprises, a good rule of thumb is increased manpower is increased output. Otherwise nobody would hire anyone and they'd just build robots to do everything.
Higher order increases in productivity do come from technological advances. But technology investment is high risk and capital intensive and productivity gains (over the short term, at least) are often smaller than simply increasing manpower. I wasn't ignoring this but for the short term, losses in manpower are typically loses in productivity.