In stating they ran parallel they meant that they're investigating the same offences at the same time. It ran parallel, but did not collaborate with, the Mueller investigation. It found more evidence and drew stronger conclusions.
“We can say, without any hesitation, that the Committee found absolutely no evidence that then-candidate Donald Trump or his campaign colluded with the Russian government to meddle in the 2016 election."
Wrong, I am quoting the bits that are taking about the US Senate Special Committee on Intelligence report.
>"the findings run parallel to the conclusions of Mueller's probe"
"the findings [of the US Senate Special Committee on Intelligence] run parallel to the conclusions of Mueller's probe"
It's reconfirming that the Senate committee findings run parallel, or in other words, come to the same conclusion, as the Mueller report.