My stance here is where the goal of the MVP is to get investment money. You're not showing your MVP to random users. You want to build something that "works" quickly, then get money to build it "properly". You have a good idea and you want to attack a certain market; but, you don't want to spend year(s) building a product and hope you can grow slowly. Your aim is to prove to investors that; you're a good team, you have a solid concept, with money you will gather a team and build this product.

In this case, I think you can(/should?!) skimp on the unit tests. The code will be thrown away after a few months of its inception.

There are of course many different MVP situations, this is just one small avenue.