Plainly, not true. Mongols ruled Russian principalities before modern Russia was established. Napoleon got to Moscow exhausted and not prepared for the severe winter. Most residents were evacuated. Russians won without fighting by leaving Napoleon starving in the empty city. Rightfully, Russians are proud of that strategy. In 1941, Hitler did not get Moscow, and Russians are proud of that as well.
Putin is hunted by Poles ruling in Moscow briefly in 1610 -1612. During the dynastical turmoil in Russia, the idea emerged that Russia could join Polish-Lithuanian Commonwealth, which at that time was a large and wealthy country. That concept had mixed support both in Poland and Russia. In the process, a relatively small Polish garrison was stationed in Moscow for about two years, and Poles had a say in political affairs there. But the Polish king, who was half Swede and not too bright, screwed it up. As a result, Poles were chased out of Moscow.
To memorate that success Putin created a new national holiday in Russia, National Unity Day.