I'm not a lawyer, nor do I pretend to be one on the internet. However I did a 20-min skim of the decision and here is my take:

Like most things, the decision is more nuanced then the headlines and hot-takes we read. But, I think your summary is pretty accurate.

Fundamentally, the recent supreme court decision was all around re-affirming that the APA was still valid and thus needed to provide claimants access to courts.

The APA (Administrative Procedure Act) - was an act of Congress in 1946 that mandated that the courts must be final arbiter of agency rule making.

Meaning, that if agency XYZ passes a rule, that it is the courts who must ultimately decide if the rule is lawful or not. (Prior to this recent SCOTUS decision, the agency itself was acting as the final decision maker - to which the SCOTUS found was in violation of the previously enacted APA law from 1946)

In a meandering way, this winds up indirectly back to the legislatures as ultimately the "rules from agencies" will now need "laws from congress" to justify themselves in future court eyes.

So yes, agencies will still be able to write whatever rule they want, but it is now up to a court to decide if its lawful or not....hopefully the threat of potential litigation will prompt more careful and restrained rule-making.