I think we should just accept the fact that MP3 is lossy compression. The lower the bitrate, the more dats is being thrown-away. And the "damage" is cumulative, even if you re-encode to the same bitrate.
Accumulated damage is the main reason to avoid MP3 during production. If you want a lossy format, you should compress ONCE as the final step. (AAC is supposed to be more-immune to multiple generations of compression.)
If you want perfection, don't use lossy compression!
But
high-quality, high-bitrate, first-generation MP3 is usually transparent in a blind ABX test (depending on the program material and the listener's ability to hear compression artifacts). A lot of people claim that MP3 compression is "obvious" but most of those people think it's so obvious that they have not bothered to do a proper, scientific, level-matched, blind,
ABX Test. The truth is with a high-quality MP3 (or AAC or AC3)
it's very-hard to hear a difference (with most program material) and you have to listen very carefully... if you can hear a difference at all.
And, (with a high-bitrate MP3) it's unlikely for anyone to hear/identify compression artifacts without the original to compare to. (Every time I thought I was hearing a compression artifact on my 'V0' MP3s made from CDs, it's turned-out that the same "defect" was on the CD.)