In the Chart for C7 he lists the 1, 3, 5, b7 notes under those column headings. Halloran assuming 1 meant the 1 chord for which C7 is the Dom 7th I guess? Not sure how or why he went there but he did. No big deal what he stated is true, but has nothing to do with the table presented. As far as sharps and flats, it all depends on the context for C# or Db etc. as for me as a guitar player, doesn't really matter what you call it, I know where it is and how it fits.

My wife asked if I had seen the dog bowl. I told her I didn't even know he could.