Long story short:
I can save the parent site of a collection as a template without any issues.
If I create a blank sub-site with nothing in it at all and then attempt to save it as a template, I get an access denied.
Yes I have full control over the solutions gallery, yes I can create items there as evidenced by the parent site of the collection saving just fine as a template.
Any ideas why this would happen? It doesn't really make any sense.
Like I said, the sub-site could be ANY sub-site, even a brand new site with absolutely nothing in it.
I CAN upload to the solutions gallery as well. It doesn't seem to be an issue with the solutions gallery permissions.
I am trying to get the tech team to look into the ULS but it's hard for them on a large farm with no Correlation ID.