The expression "to play (it) safe" means "to avoid taking risks". In a political context, it can imply that the person involved believed in a particular policy or course of action, but lacked the courage of his convictions to advocate or execute it openly.
However, the article that followed presented no evidence to show that Mukhriz believed that the "third bridge" must be built somehow, but had dialled down his statement to avoid criticism etc.
So, is the Malaysian Insider indulging in spin? In my opinion, spinning the news is totally unbecoming of any news organization that wants to be trusted by its readers.