I certainly don't speak for others, but I believe it is more about avoiding temptation as a whole for either party, man or woman. This is not to say people are just going to lunge at each other and start having sex then and there on the table, but that the person doesn't even want to put themselves in a situation that could eventually lead to more. Having a third party along (of any sex) is less intimate of a setting though and more acceptable. Being a politician, it also helps to keep in mind the optics from others. People may not know it is a business dinner and look to push a scandal for some extra clicks on their website. This seems like a reasonable way to protect his family as well. Again though, I don't know his exact reasoning, but that would be my guess.
As for the rest, I guess it is up to the person in question. Someone earlier in the thread mentioned knowing someone who wouldn't even get into an elevator with women. I imagine that is a little more on the extreme side though. I would say for others it is about being alone in an intimate environment or venturing out with that one person.
I am just curious why this is such a bad thing though when myself and others do the same as women. Not all of us do of course, but I certainly have never been given any flack for being fairly conservative in regards to business/social outings. Personally it is less about temptation though and more about awareness of the situations I put myself in.