car insurance - and towing

Just completed an online application for a quote, but had to phone to ask "does the car insurance cover a towed caravan?" (I don't mean insurance OF the caravan, but insurance covering damege BY the caravan).
Agent had to check !!!! Surely, given that it's listed as a CC-linked product, there shouldn't be a second's hesitation, should there?
Anybody bought car insurance via CC and feeling 100% certain that they are safe to tow a caravan in the knowledge that third parties are covered, please?