Why do the reporters use the technique in Chapter 9?

The reporters aren't asking the fourth source for information, per se, they are asking is they shouldn't print the story. It's a technique to garner confirmation without "confirmation".

Bernstein thought for a moment and told the man they understood why he couldn’t say anything. So they would do it another way: Bernstein would count to 10. If there was any reason for the reporters to hold back on the story, the lawyer should hang up before 10. If he was on the line after 10, it would mean the story was okay.