Thanks, P Pierce34, I knew about the Wiki on Fallout before even registering with the forum, I have done quite a bit of searching on the Internet before asking...
Gizmo, Boradam, I have done a bit of digital restoration myself and I know that you cannot invent data where there is none. A record committed to shellac or even vinyl, using the technology of '41, has no useable signal higher than around 8-10 kHz, and up to this frequency the spectrum diminishes steadily. I am not hearing that response. Also, what I do not hear is the artifacts left invariably by the elimination of clicks and pops and hiss from the material. So either The Ink Spots were recorded using a magnetic recording device that was used on the process of remastering and that tape was in exquisite condition, and the recording was made using modern microphones and hardware, or the song was re-recorded by someone sounding very-very close to the original song.
On Amazon there is a sample for the Ink Spots album from where this song was extracted and the quality is quite bad, exactly what I would expect from a gramophone record (complete with hiss, pops and cracks, and the unmistakeably sound of an early recording - be it all-electric or mechanical one).
If indeed it was quite a restoration work on an original recording, I would very much like to know more about the procedure since it clearly surpasses everything I know about restoring old recordings (and I do know a little about it).
Oh, btw, Gizmo, I do have access to professional studio software. I work as a sound engineer on a local recording studio.