"Apparently" is right; BTW didn't damage her image and public perception half as much as AP did.
No AP was the direct fruit of BTW. If Applause/DWUW had been released in place of BTW/Judas they would have both been huge smashes and on their own merits, too.
"Dope" does NOT count. The only reason it went Top 10 was because Billboard counted an ad that played by itself in front of every video for a week. It was shady as **** and I don't think it was a coincidence Bill Werde left Billboard immediately after.