The term accident is ambiguous and can include at-fault, not-at-fault, reported and unreported collisions that you, as the driver, were involved in.
A definition of an accident would be a sudden fortuitous event. The term is often used to refer to a collision or insurance event. With road rage and other occurrences that are creating granular definitions, some states are trying to add more legal language to the definition in order to make sure an accident is covered by an insurance carrier. Some states simply say it is an occurrence that is unexpected and unintended from the standpoint of the person who is injured.
As far as if a tire blowout, if it would be considered an accident (one where there is a covered loss for an insurer to pay on) would depend on if the tire blow out caused the car to be damaged or if it's just the tire that suffered damage. If it's the latter, then it probably would not be considered a covered insurance event. However, it would ultimately depend upon the terms of the driver's policy and that insurance provider's internal guidelines.
The terms of insurance policies differ, but in many cases blowouts or tire/rim damage that is not caused by theft or vandalism or is not a result of a vehicle collision aren't covered.
So, if a tire and/or rim is damaged from either theft, vandalism or a collision, then it will be up to the terms of your auto insurance policy if these items standard to the car will be covered or not. Thus, you need to read through the terms of your insurance policy and/or speak to your agent about your specific coverages.
Generally, when an automobile part, such as a tire, causes an accident comprehensive insurance would cover damages that resulted from the accident -- but not necessarily the replacement cost of tire.
If you had recently had a tire blowout, then check with your insurance agent to see if this would be covered by your policy's benefits. If not, then you may check to see if the tire that blew has any known defects which you could go after the manufacturer for.