As I tell my personal injury clients, Insurance Companies are always looking for reasons to say "NO". I feel as though it is my job to give good advice to minimize the number of reasons the Insurance Companies have.
One reason that the "low end" insurance companies use to say "no" is failure of the insured person to disclose the number of licensed drivers in the household or a history of licensure revocations. The "high end" insurance companies usually spend the time to check out the applicant to see if they qualify before writing the policy. The companies that usually write the low limits policies will write a policy for anyone and then do their research after a claim. They deny coverage or revoke the policy if a discrepancy is found post-accident.
In an application always answer questions asked by the insurance company accurately and if you do not understand, ask questions yourself and make notes of the information you provide.
Insurance policies that turn out to be worthless after your accident are worse than not having insurance, it prevents people from protecting themselves and their families and getting what they paid for.