No, of course it is not amateur built. But, our Federal Aviation Administration will class an aircraft in the Experimental class if full documentation-i.e., aircraft logs are not available or in order. Many warbirds are so classed, whether they have been rebuilt, restored or not. The classification of an American-registered aircraft appearing in this site comes from the record of that aircraft in the FAA files. These are in the public domain and are uploaded regularly to keep information current.
Your concern has been stated here in the Forum before re another foreign warbird. The Amateur built/experimental tag is a single category that may confuse the viewer, but it is a result of the FAA's classification system. Some warbirds are registered in the Standard category. These will have full documentation of the ownership trail with all aircraft logs of the aircraft in order.
I break down my photos of warbirds into several categories on my Home Page; Experimental vs. Standard is one of the breakdowns, along with make alphabetically.