Is being inherently positive healthy or a lie?

It's a matter of balance.

As you well understand, focusing on either extreme leads to problems.

It doesn't mean just look and pay attention to the positives, it means find a positive thing within everything, instead of looking at your problems as negatives, try to find how solving/ dealing with the problem will help you or someone else, and cling to that positive notion.

Well of course problems need to be solved but there has to be a balance. Dwelling all the time on the negative will just depress you.

My Mother-in-Law always says to focus on the positive and she practices what she preaches. In my opinion, she comes off as a fake person. Void of emotion. Putting on a show.