As speakers, our job is to make people think and act differently. There's no point going on stage and saying. "You know that stuff you always do? Just keep doing it". We need to challenge our audiences. We need to encourage them to challenge what they hear. Of course, that means they will challenge what we say too.
Almost everyone in our audiences are connected to the web, and will carry on using it as we speak. It will take them a fraction of a second to verify statements we make. They look at our sites, our blogs, our Facebook posts and our tweets. They form an impression of us not just from our words and actions on stage, but what we've posted, and what others have said on the same topic.
We can't get away with quoting "studies" that never happened, like the mythical "Harvard goals study" (let's not go down the Mehrabian route, we've been there many times). We can't make up statistics. We can't attribute quotes that people never made. Of course, the Internet is not an infallible source of wisdom, but it's what people refer to.
My advice is to act like your audiences. Use the web to check what you say as you rehearse. Ideally rehearse with someone else and get them to check your words. Forewarned is forearmed. One of the best approaches I've found is to say "Yes, opinions differ. This is my take on the issue , and this is why"
How do you "web-proof" your speeches?