I wrote these sentences:
The Chairman advised the Council that he had been unable to.......
The Chairman confirmed that he had met with the hotelís owner who had assured him that he was to resolve the problem.
A member complained that "that" was superfluous. Is he right?
Hi David Bentley
 The Chairman advised the Council that ...
 The Chairman confirmed (that)... optional
Here's a good rule of thumb. When that functions as a conjunction, look at the length of the phase that comes before. If that phrase is long, don't omit that as its presence helps the reader/listener navigate the syntax with much more ease.