According to the PHB Crafting can only be done if you are proficient with the tools
You can craft nonmagical objects, including adventuring equipment and works of art. You must be proficient with tools related to the object you are trying to create (typically artisan’s tools). You might also need access to special materials or locations necessary to create it. For example, someone proficient with smith’s tools needs a forge in order to craft a sword or suit of armor.
However, I seem to recall designer Mike Mearls saying you don't need to be proficient.
Q. Confused about tools in game. Is it necessary to have proficiency in any of them to use them? nope - you can still use them, just without the proficiency bonus. -M
So I'm confused, was there an addendum or is M just reversing what is stated in RAW?