Not meaningfully, not yet. They've landed the expensive part of a satellite launch system, which is very cool but the USG did it 30+ years ago. I don't think the difference between a vertical and a horizontal landing is that important.

And fundamentally there's no magic private industry pixie dust. A company is just a collection of people, as is a government; they both have to obey the same laws of physics. In some cases competition drives private industry to be more efficient. In some cases the government's long time horizons, trusted position, and ability to do things where the benefits are widely diffused make it more efficient. But it's only ever a matter of efficiency, not of can or can't.

> Receiving money from the government doesn't mean the government could have done the same thing.

It means that government money was a vital part of making it happen. SpaceX built their system on the back of $X from Musk and $Y from the USG (among other sources). If we took some money out of the X pile and put it in the Y pile, maybe the result would have been worse, maybe it would have been better.

Even the landing of the first stage was mostly based on NASA research. Which by the way, NASA had achieved long ago.

SpaceX innovated with their cost cutting, and maybe now their manufacturing processes, and by being lucky by benefitting from a period of cost cutting by NASA whereby they could hire a bunch of NASA engineers/scientists.