I think the key idea is that Rust gives you a lot of tools to encode semantics into your program. So you've got a much greater ability for the compiler to understand your semantics than in a language like JavaScript (say) where the compiler has very little way of knowing any information about lifetimes.
However, you've still got to do that job of encoding the semantics. Moreover, the default semantics may not necessarily be the semantics you are interested in. So you need to understand the default semantics enough to know when you need something different. This is the big disadvantage of lifetime elision: in most cases it works well, but it creates defaults that may not be what you're after.
The other side is that sometimes the semantics you want to encode can't be expressed in the type system, either because the type system explicitly disallows them, or because it doesn't comprehend them. At this point you start running into issues like disjoint borrows, where you know two attributes in a struct can be borrowed independently, but it's very difficult to express this to the compiler.
That said, I think Rust gives you more power to express semantics in the type system than a lot of other languages (particularly a lot of more mainstream languages) which I think is what gives rise to this idea that "if it compiles, it works". The more you express, the more likely that statement is to be true, although the more you need to check that what you've expressed does match the semantics you're aiming for.