Generally this is true, but it depends on the encoder used. Back during the huge boom of MP3 popularity in the late 90s and early 00s, it likely did make a difference, so if you're looking at MP3s that were encoded back then I would go for 320kbps every time just to be safe, but modern encoders generally do much better like you said.

These days if I were encoding an MP3 I'd use LAME at -V0 setting, letting it lower the bitrate where it can without sacrificing quality. That said, per this test from 2014 that I found as a source on Wikipedia, a 96kbps VBR Opus file is at least as good if not better than an MP3 with -V 5 as the setting on LAME with approximately a 135kbps bitrate.