Has anyone installed pavers using a mat?
Since your question asks about someone with experience in regards to pavers, and I do, I will answer this.

While with any pavers I do not recommend heavy equipment, I do not consider a car to be heavy equipment as much as I do a forklift. 

Gravel as a base is used for a foundation that withstands most shifting and prevents most sinkage. So the idea that you can only walk on this tells me it is pretty much worthless for what is being replaced. The cost of this material is high and to top that off, I can only assume laying out these mats and leveling the ground with sand will be more difficult than just leveling off one paver stone at a time over sand. 

I use pavers all the time in driveways and the process is simple. Base gravel, sand, paver, backfill cracks with sand.

I would not recommend the paver mats.