The fact that a cop gave a cyclist a ticket doesn't mean they don't have a case. Police officers look at cycling crashes entirely different than a lawyer does. When they arrive at the scene they want to know who is most likely at fault and quickly gather evidence and make a decision and often times they can be wrong.
Even if the police officer is correct that the cyclist contributed to the accident, that still doesn't mean that the cyclist can't have a claim against the driver. This is because Florida is a comparative fault state. It's possible that even if the cyclist did something wrong there still might be a big percentage of the fault on the driver.
The more serious the injury to the cyclist the more serious the claim will be against the driver and the more likelihood of success in bringing a claim against them. While the police are looking more for who mostly was at fault, a lawyer, even if the cyclist has been cited, is going to look for every percentage of fault they can put on the driver.