That is correct. I looked into Aviva's policies today and they do not have any exclusions (as to reptiles). Traders is a division of Aviva, but only deals in group policies (eg, unions, organizations, etc...).
Aviva is a broker based company, so you will have to deal with a broker. Also, they will probably refer you to Pilot, as Pilot is a subsidiary of Aviva. (If in Ontario. Pilot does not operate outside Ontario) Pilot is known as having a "Don't be cheap, the customer comes first." motto when it comes to claims.
Another line you may want to look into is the new Presidents Choice Financial line. I read that it is slowly being rolled out across Ontario this year and the rest of Canada next year. PC insurance will be operated by Aviva's Scottish & York and marketed directly through PC. It will probably be cheaper as well because there is no broker taking a commission.