All but

What does "all but" mean?

"He is all but a dawdler" means "he is almost a dawdler" or "he is all except a dawdler"?
And "failure, for them, became all but unthinkable" means "failure became almost unthinkable" or "failure became thinkable"


If “all but” means almost; then pleas look at this one:


Despite an agreement between labor and management to keep the print and electronic media _____ developments, the details of the negotiations were _____ all but a few journalists from the major metropolitan newspapers.
A. abreast of.. disclosed to
B. involved in.. leaded to
C. apprised of.. withheld from
D. speculating about.. denied to
E. ignorant of .. suppressed by
The answer is C. Despite an agreement between labor and management to keep the print and electronic media apprised of developments, the details of the negotiations were withheld from all but a few journalists from the major metropolitan newspapers.


Does it sound illogic? Because the sentence is saying: The details of negotiations were withheld from almost a few journalists (i.e. disclosed to many other journalists). Then why do we need the premise “despite the agreement to keep media apprised of developments”?


To me, it should be:
The details of the negotiations were just disclosed to almost a few journalists (i.e. withheld from many other journalists), despite the agreement to keep the media apprised of developments,
though, there's no answer.


Am I right?


Thank you in advance!