That is technically correct for a portion of the workforce.
And there's two simple cases outside of that:
- workers not paid hourly. If you're paid by the day or on another scale, commute time is wasted for both the company and the worker. Time is zero-sum after all, and in that case the company pays the same whatever happens.
- workers with external constraints (kids, health, public transport availability etc.). A worker will leave earlier if they need to commute to their kid's daycare or their doctor's office. Salary might be deducted, but if your workers are carrying their weight that's lost opportunities that are avoidable.
You just like to not commute and that conflicts with the business desire. That alone is not a lie.