faigele said the "cheaper way out," not easier. S/he means denying the claim.
If an individual has a pre-existing condition and work exascerabates it, whether it's covered under worker's comp is a matter of State WC laws. I expect most States dictate that the employer is liable but I don't know that we can say that all States do. Each State has it's own individual worker's compensation regulations.
As far as whether the WC carrier denies the claim in most cases, that's really not relevant. A WC carrier, who is the agent for the employer, is liable for the injury or illness if it can be demonstrated that work caused the ailment. If you're standing in an aisle at work and a forklift hits you, causation is obvious. If you claim that your sore back is due to work, you have a history of pre-existing back problems, and the type of work you do does not necessarily lend itself to obvious exposure (i.e. you're not lifting 100 lb. sacks all ay long), that's a lot more difficult to determine. Establishing causation would depend largely on the person's medical history, the type of work, the specifics of the current injury and so forth. The carrier investigates, obtains all the relevant medical reports and history and makes a ruling. If the individual disagrees, they may file for hearing with the State's Worker's Compensation Division.