Houseman and Harmon have a contract with the Kentucky State

Houseman and Harmon have a contract with the Kentucky State Police to train forensic lab specialists. The state police received a large federal grant as part of the economic stimulus package, and decided to use the grant to train more forensic lab specialists for the police crime lab. Rather than solicit bids from companies interested in conducting the training, the state police awarded a no-bid contract to National Forensic Science Center, a Florida company. Houseman and Harmon wrote a letter to the director of the police crime lab criticizing the no-bid contract as overpriced and a waste of taxpayers' money. They also sent a copy of the letter to the local newspaper, which did a story on the no-bid contract. The director of the crime lab then suspended Houseman and Harmon. They claimed that their suspension was in retaliation for their letter about the no-bid contract, and was a violation of their First Amendment rights. Was it? Explain.