There are many inaccuracies in this article.
First, not all brokers are direct clearing members, i.e. not all brokers can clear & settle trades directly with the DTCC. Some brokers will use a clearing member as an intermediary to help them clear & settle their trades. I don't know what RH does, but generally, a broker as big as RH can be a direct clearing member with DTCC since they can afford the capital & collateral requirements.
If RH is not a direct clearing member, which means it clears & settles it's trades using another direct clearing member, then if DTCC raises the collateral requirements for clearing & settling certain stocks won't necessarily hurt RH, unless the clearing member they use also followed suit and raised the collateral requirements for RH (In many cases, the RH clearing member will cover RH in the form of an overnight loan so that RH doesn't have to come up with too much capital in a short period of time).
Second, the clearing house (DTCC) can't really raise collateral above 100% (for long positions).
Third, the statement in the article saying that you don't own your shares is false and naive. The system works on a central depository and many custodians connected to that central depository. When you buy shares through your broker, those shares gets registered with the custodian your broker is working with (some brokers work with multiple custodians).
Your broker informs the custodian that you bought 100 shares in AAPL and also clears & settles the trade with the DTCC (either directly or through one of the other clearing members). The ownership of shares @custodian level remain pending until they receive trade settlement from the DTCC, then it becomes confirmed and your custodian now is officially holding the shares on your behalf (In return for a very small annual fee, it's not free).
The DTCC is at the center of the financial settlements & clearing, however, they don't own any shares. The DTCC ownership records must always match with the custodians.