* Li through to third round
* Beats Swiss teenager in straight sets (Writes through)
By Ian Ransom
MELBOURNE, Jan 15 (Reuters) - Disillusionment with negative reporting in her home media nearly saw Li Na give up the game last year in the wake of her early French Open exit, the Chinese number one said at the Australian Open on Wednesday.
Li, who won the 2011 French Open to become Asia's first grand slam singles winner, suffered the criticism after being bundled out in the second round at Roland Garros by American Bethanie Mattek-Sands.
China's trailblazer Li has long endured a sensitive relationship with her country's media, which has been quick to condemn as well as heap praise on their most successful player, but the critical reports that dogged Li in the leadup to Wimbledon took their toll.
"It was a very negative thing," Li told reporters. "I could say something but (what) they would write down in the newspaper was totally wrong.
"They make me very - they gave me a very tough time when I played the French Open, and it continued to Wimbledon.
"It's not (all) the Chinese media. It's some of them.
"But someone, maybe they wanted to be more famous, you know, so that's why they always write down something I never said or another way round.
"But I was really happy (to) do well in Wimbledon, so that's why I continue until now. Otherwise I don't know where I am now," she added smiling.
Following the French Open, Li boarded a long-haul flight to her home-town Wuhan in central China to see her mother and galvanise herself for Wimbledon, where she shrugged off her slump to reach her third quarter-final at the tournament.
Her first run to the U.S. Open semi-finals ensued and Li finished off her best season since her breakthrough 2011.
Runner-up at Melbourne Park last year and in 2011, Li moved into the third round on Wednesday by fending off 16-year-old qualifier Belinda Bencic 6-0 7-6 (5) under a blazing sun at Rod Laver Arena.
Hailing from Wuhan, known colloquially in China as one of the Yangtze river's 'three furnaces' due to its sweltering summers, Li was more ruffled by her occasionally misfiring forehand than the heat at Melbourne Park, where temperatures were nudging 40 degrees Celsius (104 Fahrenheit).
"I think I was lucky, you know, because at least they put me in the first (session). So I can finish the match before 1:00 p.m.
"Yesterday, I was practising earlier to try to play little bit in the heat."
Li will play Czech 26th seed Lucie Safarova next and a run to the second week of her favourite grand slam is likely to keep the headlines positive in China.
Li, nonetheless, pleaded for fair treatment.
"Please don't try to make me wrong again because, right now, I really, how do you say it, I am trying to be friend. But maybe not everyone thinks about that." (Editing by Patrick Johnston)