@oristarA,
If you want a simple rule, the use of an indefinite article "a" is used to talk about something in general, non-specific, or non-particular.
Since the cause of death is unknown, the statement "She did not provide a cause of death" suggest an unknown cause or in other words does not specify a certain cause. It could be any number of causes, thus the use of an indefinite article "a" to go for a general statement and to modify the non-specific noun.
Now, say, for the sake of giving you an example, if the cause of death was known to be third degree burn from the fire, then the reporter would likely would have worded the statement "The cause of death was third degree burns..." instead of "A cause of death was third degree burns..." In this case, you see that the use of definite article "the" makes more sense, and is used in such a case to refer to a particular noun.