The drain tube for the HVAC system might be partially clogged. This will cause exactly the symptoms you describe. If condensation from the AC evaporator, or water from a rain storm, overwhelms the drain tube's ability to carry it away, the water will drip onto the carpet instead of onto the road.
The drain tube is on the firewall, low on the passenger side. You'd probably have to raise the car to see or reach it. This is probably the "cowl drain" that was suggested to you.
A clogged sunroof drain tube is another possibility.