"If they won't say who they are then how can the news media quote them and how do you know what they really said."
Are you new to politics?  There are a lot of unwritten rules to reporting politics.  For example, journalists know who they are talking to and could, if they chose to end their career, burn them and print their name when "off the record."  But that would also affect the trust of other sources to provide information off the record, ie. one of the fundamental purposes of having freedom of the press and protection of sources requires a pretty high hurdle in the courts or to put it another way it is "in the public interest" to protect sources.
If you only equate truth value to complete disclosure we probably wouldn't have had Watergate or the Iran-Contra affair or any number of presidential indiscretions come to light.  You rely upon reports from "a senior official" based upon the credibility of the news source which has to be earned.