Our ears are burning.Twice in two debates, Democratic U.S. Senate candidate Patrick Murphy invoked our name as a shield in the face of criticism from Republican incumbent Marco Rubio about his background."You continue to throw out these lies. They have all been debunked by PolitiFact," Murphy said.Murphy's response was memorable — especially to us. His retort is a wishful reading of our reports. Here's the truth: Murphy has exaggerated his credentials, and his opponents have also exaggerated their attacks on Murphy.In last Wednesday's debate in Davie, Rubio dubbed Murphy a "serial embellisher," saying the South Florida congressman never had a contract to clean up gulf oil, and he could not have worked as a CPA in Florida because he didn't have a Florida CPA license.ABC's Jonathan Karl, the moderator of the first debate, also asked Murphy about his background."You've described yourself as a small-business owner, but your company is a subsidiary of a billion-dollar construction firm founded by your father. You call yourself a certified public accountant, but you have not been a CPA in the state of Florida. And for more than a year, your website said that you had two degrees from the University of Miami, when in fact you only had one.""Absolutely not," Murphy responded, "and I am glad you asked this question, and it's important that you all hear it from me. You see, PolitiFact, an independent fact-checking agency, has already debunked these accusations."No, we haven't.Words matter, and here's why.In September, we fact-checked a TV ad from the National Republican Senatorial Committee that made less nuanced attacks about Murphy's résumé than what was described at the debates. The attacks skimmed the facts laid out in a June investigation into Murphy's background by WFOR-TV in Miami.The ad starts with a clip of Murphy saying in 2012, "I believe that my background as a CPA and a small business owner is exactly what we need."The narrator then reads lines from a WFOR-TV report and says, "Never worked as a CPA," and "Never a small business owner."Those words rated Mostly False, meaning they contained an element of truth but ignored critical facts that would give a different impression.The ad made it sound like Murphy flat-out lied about being a CPA. He is a licensed CPA — in Colorado. He could not sign off on audits at his Florida job because he didn't have his Florida license, but he still was a CPA.Murphy's claim of being a small-business owner is complicated.Murphy's business, Coastal Environmental Services, was owned by multiple people and stemmed from a business his father owned, Coastal Construction. Annual reports show Murphy was a director in 2011 and 2012, though he remained an owner and not a director since winning election to Congress in 2012.Unlike the slippery TV ad, Karl didn't say Murphy was never a small-business owner; he started his question by noting his father's connection to the business Murphy claimed. Still, Murphy said PolitiFact had debunked the accusation.PolitiFact Florida also didn't rate Rubio's statement about Murphy's company not having a contract to clean up the gulf oil spill. We visited the issue in a June explainer to attacks against Murphy, laying out that Murphy's Coastal Environmental Services didn't get the contracts itself, but worked with and then bought another company with existing contracts. Murphy's actual work in the gulf was short-lived, just a matter of months.Finally, we didn't debunk an attack from Rubio about Murphy's degrees from the University of Miami — we actually backed it up. When Rubio's campaign released an ad claiming "Murphy embellished, according to reports, his University of Miami academic achievement," we rated the statement Mostly True.Murphy's campaign websites for U.S. House and Senate used to say he had "dual degrees" from Miami, but what he really had was a single bachelor's degree with a double major in accounting and finance. Murphy's campaign fixed the error.There's a lot of blame going around, but here are the facts: Murphy puffed up his qualifications. Republican attack groups exaggerated the scope of the issue.But Murphy's claim that we debunked every attack leveled against him?That's also exaggerated.Contact Katie Sanders at [email protected] Follow @KatieLSanders.