You're forgetting, Doug, that the MP2 you started with was very high quality to begin with. The radio station automation software uses that format because those files are so good (and they are pretty large, too, if I recall correctly).

The problems with artifacts-piling-on-artifacts is mostly a problem when you take a lower bitrate MP3 (like say, 128) and attempt to perform edits and re-encode at a low bitrate (like 128).

As with any lossy compression scheme, the higher you crank the "quality" slider, the less artifacts you notice. This is true of any generation of recompression, whether it be the first or the tenth. The lower the quality slider, and+or, the more generations, the more noticeable artifacts become.

Also, you are clouding the issue by calling the MP3 fourth generation. It's really third generation in terms of compression:

First generation: Original CD, or any properly-made digital rip of that CD in WAV format.

Second generation: The MP2 file encoded from that WAV, or any exact digital grab of the output from that MP2, such as a written-to-disk WAV of that MP2.

Third generation: The MP3 file made from that WAV.

Now, take that MP3 file and run it through a couple more generations (perhaps even only one more generation) and, depending on the material, you will hear artifacts. Being familiar with the song, it's not one of those songs where you're going to notice artifacts very soon. It's a bad test song. But there are certain songs which will show artifacts on the first 128k encode, let alone the second or third.