It is true and it is terrible. Woe to be a programmer. The Church-Turing Theorem implies it is almost impossible for any languages exhibiting recursion to not be (Church-)Turing Complete. It is easy to forget how deeply, darkly, and deceptively simple the Lambda Calculus is. It is easy to forget that anywhere you may splice in something that even gently resembles the Lambda Calculus you may draw out the frightening runes of the many eldritch combinators many of which are indeed subject to accidental infinite recursion and The Halting Problem. (Including the infamous Y combinator.)

I have seen the Typescript "computing this type lead to what appeared to be infinite recursion and I gave up" errors. The compiler is well built, it mostly does not truly crash in an exceptional case like that, but it does have to use hard, practical heuristics to avoid getting stuck in infinite loops (including harsh stack depths and calculation timeouts for type checking).