Mid-ranges have better glide and thus slower drop rates than putters. What is happening is that players who have little confidence with their putters are not able to find the sweet spot where it will have the proper glide with the proper power needed. You are scared of over-powering the putter because with any disc, the more power you apply, the less accurate you become. By using a mid, you can dial back on the power and thus have greater control.
The problem with putting with a mid is that since they have better glide; if you miss you are more likely going to miss further away than if you were to miss with a putter. Because putters have faster drop rates than mids, they will stall closer to the basket. This is crucial if you are making a long distance putt you do not anticipate making and thus want to at least land close for an easier second putt.
Putting with a putter is not a rule. You can putt with anything you like. However, some tournaments require that you declare before the round what disc is going to be your putter. I believe this is an older rule that has been removed, but I have heard of some more competitive leagues and tournaments that still require this.
If you feel more comfortable putting with a mid, go for it. Like I said earlier, it has a slower drop rate which means that it glides perfectly with the power you feel comfortable giving it. When I get in a putting funk, I have no qualms switching to my Star San Marino Rocs or my Star Ontario Rocs. In the past I have also used my FLX Drone and Z Buzzz. Heavy TeeBirds work well and I have a friend who almost exclusively uses his FLX Avenger SS for putting.