This is not true, DisplayPort and HDMI is not compatible, but the dedicated converter chips are quite efficient at their job. One is present inside every USB-C to HDMI cable, dongle or dock, as there is no such thing as USB-C HDMI alt-mode. Heck, even laptop HDMI ports are usually implemented through a DP converter.

You might be thinking of DisplayPort++, which is a special port supporting both DisplayPort and HDMI, allowing passive adapters. This is not available in the USB-C DisplayPort AltMode.