FWIW, I thought I would take a look at this.
I tried loading and playing test.mp3 in Audacity and in VLC. There is significant overmodulation in Audacity. When the Audio is loaded into Audacity (drag-and-drop), the Amplify effect uses -18.051 to bring it down to full scale - go figure! When I look closely at the peaks, there is apparent damage, but they are not flat as I might have suspected. And upon playing, the audio still sounds heavily damaged.
However, when I played test.mp3 in VLC 3.0.12 (windows), the audio played clearly and there was no distortion whatsoever.
I tried DVDdoug’s suggestions:
FFmpeg import into Audacity: audio is heavily clipped at 1.0 as one might expect, so unlike Audacity import, no change with Amplify effect. Curiously, audio “sounds” much closer to VLC than to Audacity’s import, but sound seems bassier and muddled.
Tried Kabuu Audio Converter: this was identical to FFmpeg’s import. The only difference was dither. inverted this track, then mixed it with the FFmpeg track and found only about -90dB signal remaining.
Tried TAudioConverter: I had an installation error (BASS.dll not found) (both 32-bit and 64-bit versions).
So curiously, I tried playing the mp3 file via VLC and recording with Audacity. Here is what I saw:

Top = VLC, Bottom = FFmpeg. Note that the VLC curve does not clip. So it appears that VLC has some “magic” code the others do not have that fixes the problem.
===================================== 
MP3Diags (unstable) 1.501 reported:
====>MP3GAIN_MINMAX=“122,238”, MP3GAIN_UNDO=“-028,-028,N”, REPLAYGAIN_TRACK_GAIN=“-5.330000 dB”, REPLAYGAIN_TRACK_PEAK=“6.618240”<=====
*No ID3V2.3.0 tag found, although this is the most popular tag for storing song information.
*ID3V2 tag doesn’t have an APIC frame (which is used to store images).
:padding=0, unsynch=no; frames: TSSE=“Lavf54.20.4”
:MPEG-1 Layer III, Stereo, 44100Hz, 48000bps, CRC=no; [Xing header info: frame count=134, byte count=56162, TOC present]
*Low quality MPEG audio stream. (What is considered “low quality” can be changed in the configuration dialog, under “Quality thresholds”.)
:0:03, MPEG-1 Layer III, Joint stereo, 44100Hz, 128000bps CBR, CRC=no, frame count=134; last frame located at 0xd9e1
===================================== 
VLC has some “magic” code the others do not have that fixes the problem. Keep smiling. 