I made a baseplate for my 09 Pontiac Vibe (same as a Toyota Matrix) with BlueOx compatible connections. I use it with a RoadMaster tow bar with optional BlueOx connectors and no crossbar.
My Vibe has a substantial aluminum extrusion (bumper) behind the front facia. My baseplate fastens to that as well as the frame of the Vibe and it provides lateral support much the same as a crossbar. Your CRV may have the same setup.
I've been towing for two years with no problems.
97 Aerbus XL3250, 06 Honda CH80
DIY Banks, track bar, acoustic insulation
Koni FSD front/Bilstein rear