Two civil lawsuits against the company that owns the private jet that crashed Sunday in northern Mexico -- presumably killing music star Jenni Rivera -- accuse the firm of lying about its links to a businessman convicted of falsifying maintenance records.

Insurance firms QBE and Commerce & Industry Insurance Company filed suits this year seeking to rescind its contracts with aviation company Starwood Management because of alleged falsehoods.

In short, the insurance companies claim that Starwood lied in its application for coverage about the history of the planes being insured and about the true owner of the company.

Starwood is the owner of the Learjet that crashed Sunday in Mexico, most likely killing Rivera, who has not been found. DNA tests are currently being conducted to confirm the identities of the remains found at the crash site.

Rivera was a Mexican-American star with a rising cross-border appeal. She sang traditional Mexican ballads and was nominated for a Latin Grammy Award in 2002 in the category of "Best Banda Album."

The lawsuits against Starwood focus on the man who signed the insurance paperwork on its behalf, Ed Nunez. Nunez's full name, the insurance companies claim, is Christian Edward Esquino Nunez, a businessman with a criminal record that includes falsifying airplane records.

The registered owner of Starwood, Norma Gonzalez, or her representatives were not immediately available.

In an unrelated lawsuit, Starwood admits that the company gave power of attorney to Ed Nunez to sign documents but denies that the man has any ownership or management role in the company. The sole member of Starwood is Norma Gonzalez, the court document states.

The pair of lawsuits from the insurance companies, however, tell another story.

The QBE lawsuit claims that Ed Nunez, also known as Christian Esquino, is the "alter ego" of Starwood, and that he is tied to the operations, assets and ownership of the firm in a way that makes him "inseparable" from the company.

The convicted businessman's history may be troublesome to observers of Sunday's crash.

Additional court records reviewed by CNN show that under the name Eduardo Nunez, the businessman was indicted by a federal grand jury in 2002 of falsifying logbooks to obtain airworthiness certificates from the Federal Aviation Administration. He pleaded guilty.

Esquino, a Mexican national, pleaded guilty in 2004 of participating in a scheme in which he "obtained a counterfeit Mexican inspection stamp, which was used to make entries in the fraudulently created logbooks, concerning the airworthiness for aircraft engines, propellers and airframes, as well as, certify completed 25-, 50- and 100-hour aircraft inspections," the criminal complaint states.

He sold those planes at a higher price, according to court records.

The Learjet in which Rivera was traveling, built in 1969, was not one of the aircraft cited in any of the legal action, records indicate.

Another case filed against Esquino in 1993 resulted in a conviction for "the concealment from the IRS of the existence, source and transfer of cash" for which he was sentenced to five years in prison.

According to court documents obtained by CNN, Esquino has a criminal record dating to 1991, when he pleaded guilty to one count of "aiding and abetting a false loan application." He was then sentenced to three years on probation.

In April 1991, Esquino was arrested and subsequently indicted on one count of "conspiracy to possess with intent to distribute cocaine," according to court records. He pleaded guilty.

The insurance companies claim that they would not have provided coverage for Starwood if they had known about such a criminal history. They allege that Esquino simply went by the name Nunez instead and failed to report his past.

Civil aviation officials say they believe no one survived Sunday's crash. Yet Rivera's family says hope is the last thing to go.

Authorities would not describe the condition of the remains but said they do not know how many people they belong to.

The remains were found Tuesday at the site of the wreckage and were transported to Monterrey, the same city the private Learjet took off from, said Priscila Rivas, spokeswoman for the state's public ministry.

It is too early to tell if Rivera's remains were among those found, Rivas said, but DNA tests are under way. Test results could take anywhere from a day to weeks, she said.

Rivera's brother, Lupillo, arrived in Monterrey Tuesday from the family's home in Lakewood, California. Before he left California, he described the situation as "95% bad news" but added that the family is clinging to the small hope that Jenni Rivera somehow survived.

A makeshift altar with flowers, balloons and candles appeared on the family's front lawn.