Sadly, the news about the CR-V is true. In 2015 the CR-V went to a CVT (Continuously Variable Transmission), which cannot be flat towed. Shame as it is/was such a popular tow vehicle. Thank you Honda.
From the 2015 Honda CR-V owner's manual:
You may still be able to tow a CRV 2WD version on a dolly, but then you are looking at probably 4,200lbs or so. You are not going to be able to tow an AWD version on anything but a trailer.
I had to get rid of my Nissan Maxima when I bought the RV because it had a CVT and could not be flat towed.