Yes, it's difficult to follow exactly what they did. This:

> We used 10 fake Facebook pages with no content, and changed the “paid for” disclosure after each senator was approved.

Makes it sound to me like they got approval using a real identity and then changed the now-approved account to use a different name.

Methodology aside, though, Facebook shouldn't be showing that they verified the identity if they did not verify the identity. Unless the methodology was "we stole the identities of some senators" or "we cracked their passwords", this is a failure a another breach of trust on Facebook's part.