Ignoring the symbols is exactly what is meant by "the grammar" of a sentence. Two things are grammatically the same if they use the same grammar productions when parsing/producing.
This isn't conveniently bending definitions to make myself sound correct. This is the specific technical definition that was worked out by linguists in their empirical examination of language (and later adopted by computer scientists because it happens to work nicely with programming languages too). It might not match with some colloquial uses, but it's a reasonable assumption that an article discussing linguistics would be using the precise linguistic definition.
This isn't conveniently bending definitions to make myself sound correct. This is the specific technical definition that was worked out by linguists in their empirical examination of language (and later adopted by computer scientists because it happens to work nicely with programming languages too). It might not match with some colloquial uses, but it's a reasonable assumption that an article discussing linguistics would be using the precise linguistic definition.