If you look through the entire search data package you'll find that the water bottles were placed there by a regular hiker to the area. He drew the rangers a map of where these bottles were found and were some others were stashed. This was described in detail. So the found bottles had nothing to do with Bill. Also, the coordinates for the bandanna are in there, listed twice I believe.
The fact that the dogs went off on the water bottles brings into question the reliability of the dogs. The bottle were secreted off the trail where Bill could not have found them and handled them. The dogs also showed great interest in an area that was searched very well, with nothing found but a Big Horn carcass.
A hot, dry environment, several days after the fact, and having the area trod by many individuals is almost an impossible situation for a dog.
The bandanna could have been checked for DNA or inquiries made if it was one Bill owned or purchased at REI shortly before his trip (REI keeps records of all member's sales if their number is used.....Sort of like a coop version of PRISM). To my knowledge none of this was done.
So while the water bottles definitely had nothing to do with Bill the bandanna could. Or may not. No one knows. But personally I'd attribute little to no weight to the report that the dogs went off on it.