Could it be that other trading platforms use the same clearing firm?
For a small brokerage, they would have to work with other brokerages to help them trade, as they wouldn't have enough shares they already hold to trade them within their users. So Robinhood asks Apex for more shares, and Apex has to ask HSBC/Fidelity/JPMC/Goldman if Apex doesn't have any. At some point, all the other institutions also don't want to give up their shares because they need to satisfy demand from their own users. Trading with other firms tends to be really slow too.
It's a short squeeze too, by definition there's not enough stocks available for everyone who wants to buy. So some firms ran out and couldn't get more.
That's... not how stock markets work. For every buy there must be a seller. If there are too many buyers but not enough sellers the price simply goes up.
https://blog.robinhood.com/news/2018/10/9/introducing-cleari...