If you look through papers from that era I don't think you'll find that's true at all. You could fairly say that only a few of the prominent labs from the first neural-net boom lasted long enough to still be prominent labs now in the second neural-net boom (though even then there are several: Hinton, Bengio, Schmidhuber, LeCun, etc.). Since they're still around doing interviews and putting out new papers, understandably their work has a higher profile now than that of people who aren't in the field anymore. But there have been a ton of others over the years too, just many of them from the first wave have moved on or retired by now.
Especially in the '90s the field was hot and reasonably large (and it was pretty easy to get funding, too). If you look at e.g. the NIPS 1992 proceedings, it's definitely not just a handful of labs: https://papers.nips.cc/book/advances-in-neural-information-p...