Whether you consider NEA to make their barrels or not depends on what you consider "making the barrel". They source blanks from a particular manufacturer (who I would actually say is NOT well known...but very desirable) and profile etc themselves.
So if you're someone who says "Noveske don't make their own barrels" then you're also someone who would say "NEA don't make their own barrels".
Most companies buy blanks and go from there. Colt has done it a lot, for example, depending on their production demands.
They have had some sketchy parts runs - specifically the more stuff they outsourced the more problems they had. They did have an issue with a particular bolt supplier and the results are seen above. Their current stuff is quite good IMO. If you can get current production parts, I think the quality is quite high.