Wider tires offering faster speeds and safer ride? I'm looking at riding again. I took a two year break after I crashed going down a hill when a tree branch was down and I went over my handlebars.

I've always assumed that thinner tires were better for riding but I was watching this video from Global Cyclist Network. In the video the rider makes a strong argument for wider tires.

What I'm wondering is there any literature or empirical studies that are public that show these results? I found some small things that corroborated this but I was sure this would be the right place to ask.
Depends what you mean by 'better', and under what circumstances. The major tire considerations are, in no particular order:


Drag or resistance
Comfort
Grip
Durability / puncture resistance
Mass
Aerodynamics


What constitutes a 'better' tire for you depends on your preferences and what kind of riding you want to do.

The hypothesis that GCN puts forward in a few of their videos is that narrower tire width and higher pressures do have lower rolling resistance on a smooth surface, but wider, lower pressure tires actually offer less overall drag over irregular or bumpy surfaces because they have less suspension losses.

The idea is that because wider tires don't necessarily have more drag you can run  wider tires and get better grip and comfort without a penalty.

GCN did some relatively well controlled experiments on cobbled surfaces. Here is a video that talks about what they did and the results they got: 
                
            

Some more experiments on bumpy surfaces: https://janheine.wordpress.com/2016/06/14/suspension-losses-confirmed/