Whether or not they are a debt collector under the statute is not determined by their stated field of business. It is determined, pursuant to FDCPA 803(6)(F)(iii), by whether or not the debt was in default at the time they acquired the debt. That section of the FDCPA states that if a debt was not in default when it was obtained by a party, they are not a debt collector under the statute.
A factor is nornally one who purchases accounts receivable in good-standing from a creditor, thus providing the creditor with instant cash, and relieving them of any further efforts to collect the debt. The factor takes over as the recipient of future payments on the debt. In such cases, they are not a debt collector.
Reporting as a factor implies that they purchased the debt in good-standing, but if your specific debt was delinquent at the time the acquired it, then they are a debt collector, regardless of the moniker they operate under. Nothing precludes a factor from purchasing a debt in default, so dont get hung up on their general stated field of business.
They use their factoring company moniker to imply they have become a creditor rather than a debt collector, even if the debt was delinquent when purchased.
If that is your situation, they are misapplying their status.
