The most common and most likely answer to this crossword clue is the 6 letter word LEAKED
I've seen this crossword clue in Independent
L
E
A
K
E
D
More clues leading to the result LEAKED
Buddy explains!

The straight part
We know that "Gave story to the media/not watertight" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case gave story to the media/not watertight = leaked.The cryptic/wordplay part
In cryptic crossword there's often an wordplay/cryptic part as well.This part involves a more complex hint, such as an anagram, homophone, hidden word, etc.
Sadly, We don't have an explanation for this specific crossword clue yet.
What does LEAKED mean?
LEAKED verb- To allow fluid or gas to pass through an opening that should be sealed.
- (of a fluid or gas) To pass through an opening that should be sealed.
- To disclose secret information surreptitiously or anonymously.
- Of a document, etc, produced by a company or organization, intended to be confidential but having been released to the public or the press.