Sounds like our '05 Ody. Before buying it to tow four down I called Honda and they said it was towable four down, do you want that in writing? I said yes and was lucky I had it. Took it to RoadMaster and they used it for a test fitting. Towed it 300 miles and started seeing that Honda said no to towing it.
After some back and forth involving the WA and CA AG's offices and showing them the letter Honda decided to send us a check for $2,300. So we bought a KK-460 dolly and used it for a few years. But we saw others towing the Ody's four down, talked with them and all reported having no problems, so about 4 or 5 years ago I went back to four down and haven't had any troubles.
So, it seems Honda was playing it safe by saying no to four down towing. BTW, always remember to release the parking brake before towing, even on a dolly!
2009 45' Magna 630 w/Cummins ISX 650 HP/1950 Lbs Ft
Charter Good Sam Lifetime Member, FMCA, SKP
RV'ing since 1957, NRA Benefactor Life, towing '05 Odyssey