I dont think DD being gay does have anything to do with anything, it came about in an answer to a question asked during her US tour:
I'll post a quote from the linked report in the OP. Here goes:
"She took audience questions and was asked if Dumbledore found "true love".
"Dumbledore is gay," she said, adding he was smitten with rival Gellert Grindelwald, who he beat in a battle between good and bad wizards long ago.
The audience gasped, then applauded. "I would have told you earlier if I knew it would make you so happy," she said.
"Falling in love can blind us to an extent," she added, saying Dumbledore was "horribly, terribly let down" and his love for Grindelwald was his "great tragedy".
As an avid fan (just thought I'd add that in case you didnt know ) it personally leaves me with a much greater understanding of the characters early life, why he took ages to face Grindelwald etc.
Oh hermiones gadget was called a Time-Turner!