Some of those privately offered investments are also publicly quoted on the public market.
Absolutely correct.
There have apparently been public quotes on the OTC market for a few of the Grayscale Trusts that were made available through private placements. On the OTCQX Best Market, individual and institutional investors may also trade the Trusts' shares publicly.
https://www.grayscale.com/crypto-productsSpeaking of those funds, it is absolutely mind blowing how they are trading: none at NAV, BTC and ETH at discount, ETC at huge discount, while other LINK for example at an astonishing premium.