No, an out of court settlement is still typically handled by lawyers, it just means the lawyers (possibly with clients present) get together outside of the court and reach an agreement, vs going to court and trying to convince a jury/judge who should get what.
This appears to be describing a situation where the defendant goes to the plaintiff out of court and presumably without lawyers. Possibly just skip his own, but more likely skip both lawyers.
But the risks are, as stated, that the plaintiff could take the money and not drop the suit. “What do you mean you paid? Where is the contract?” Etc. Also, the lawyers generally have something in their contracts to get paid.
Also, if you couldn’t reach an agreement such that you needed lawyers in the first place, it’s hard to see reaching an agreement without the lawyers later.
With respect to the free speech issue on TGW, I took the argument to be that every word appearing on CEO/Owner’s search engine is protected speech, maybe even commercial speech and therefore the thought process or in this case, the algorithm, used to produce it is protected. I don’t think I am explaining this clearly, but maybe it is just that defendant has no right to see the algorithm that produces inaccurate results, that defendant has a right to produce a crummy search engine without having to disclose his methods. From a legal standpoint I have no idea if this makes sense, but it did not arouse my curiosity in the same way the end run around plaintiff’ attorneys did.