As this is such a highly viewed forum discussion, I wanted to add some references here that may be useful.
As @jakefowler alluded to earlier in this thread, the mesh environment has arrived in Fusion 360. In the July 27, 2016 Update for Fusion 360 the new environment was released.
You may notice that in the Preview panel of Fusion 360, there is a Mesh Workspace preview.

Enabling this preview will give you access to a the Mesh environment in Fusion 360.
Please note that this screenshot is taken while in a Direct Modeling design (no parametric timeline):

If you would like to access the Mesh environment while in a Parametric Timeline design, use the familiar Insert > Mesh command to insert a Mesh body into the design. Afterwards, you can right click on the Mesh in the Timeline and select Edit to access the Mesh Environment

One you're in this Environment, there are a bunch of tools you can use in the Modify drop down menu to edit the mesh body.

Some other cool videos involving Mesh files, Remake, and Fusion 360 that are helpful are below. I note that if you can convert a mesh to a quad OBJ file format in Autodesk Remake, you can then convert to T-Splines and then finally to B-REP geometry for some nice looking designs that you can even Mill.
Autodesk ReMake & Fusion 360 - Physical and Digital Prototyping
Autodesk Remake and Fusion360 - Improving Existing Designs
Fusion 360: STL to CNC Machining with Autodesk ReMake
I hope this helps!
Nathan Chandler
Principal Specialist