Not exactly true. Even out of the box and only set to auto, a mirrorless will take better auto shots than a p&s because of the bigger sensor and better depth of field (e.g. for things like getting nice background blur). For that matter, a DSLR will take better auto shots than a mirrorless in most cases too. I know some people who just use their DSLR as gigantic expensive P&S+1 for s95/s100. If you are going to be in auto mode anyway, its quite pointless to get the more expensive interchangeable lens cameras.
The consideration is whether you have the budget and don't mind the bulk, because a mirrorless will be bigger than a P&S (unless you go for the cheapest m4/3 pancakes, which will also have the least difference in image quality). If your answer is yes to both, definitely why not go for mirrorless.