It's possible to be both liberal and rigorous in what you accept. Let me provide a motivating example.
Let us say you have a tool which is nominally supposed to accept JSON, but for whatever reason you might expect a lot of format errors in the JSON: comments which aren't legal, trailing or missing commas, an equal sign instead of a colon, unquoted symbols as keys.
If you build some kind of shotgun system to try and repair the JSON, you're going to have a bad time. What if, instead, you define a grammar for your liberal superset of JSON? Now there's no ambiguity about what you accept, or what your parser will do with a given string: it's as well-defined as JSON is, it just accepts more formats of the 'same' data.
If your system only ever emits strict JSON, well, you've embodied Postel's law: this is liberal in what it accepts and conservative in what it provides. While still losing none of the rigor of accepting well-defined formats.