The perspective gets a bit lost here: "Medical practice client received a 1099 that includes Accounts Receivable that was purchased."

The person getting a 1099 would be the person selling the AR. They sold their asset.

The people buying the AR bought an intangible asset. As they collect, their Asset value gets reduced. Essentially, it's an intangible inventory at a discount (COGS).

"the best way to deduct the purchased A/R"

The people posting AR as deduction are not the 1099 party. The people collecting the AR have a reduction in their asset (the AR) as they collect income against it, and the cost basis is like a COGS event. AR is more like a goodwill asset, though; not inventory.

It's not factored if it was sold. Factored is leveraged.