Scots is somewhat partially intelligible in written form to English speakers, but that does not make it the same language as English. You might as well say that Spanish and Portuguese are the same language.
There's also a smooth language continuum between Spanish and Portuguese, with varieties like Galego. This doesn't make them the same language. Historically the language continuum encompassed most of Europe, but people at the extremes would've had no expectation of understanding each other's language.
