And because Mueller said that he could not establish there was a conspiracy, Barr said there can be no obstruction.
We will learn more in the coming days about why Barr made the decisions he did, but taking Barr at face value, based on the actual letter he wrote, what you wrote isn't correct.
This isn't your fault though. Barr and Trump's other political allies have been intentionally vague about communicating Barr's rationale.
While this bogus legal argument -- one that is not in any way supported by the case law -- was indeed pushed by Barr at various moments prior to him becoming the AG, in his letter summarizing Mueller's report, Barr didn't push that particular legal argument (probably because it's so incredibly weak and unconvincing). Instead, what he did was say that because conspiracy could not be proven then it would be difficult to prove intent with respect to obstruction.
Read it for yourself:
The letter, by Attorney General William P. Barr, details the main findings of the special counsel’s two-year investigation into Russian interference in the 2016 presidential election.
www.nytimes.com
In making this determination, we noted that the Special Counsel recognized that “the evidence does not establish that the President was involved in an underlying crime related to Russian election interference,"
and that, while not determinative, the absence of such evidence bears upon the President's intent with respect to obstruction. Generally speaking, to obtain and sustain an obstruction conviction,
the government would need to prove beyond a reasonable doubt that a person, acting with corrupt intent, engaged in obstructive conduct with a sufficient nexus to a pending or contemplated proceeding. In cataloguing the President's actions, many of which took place in public view, the report identifies no actions that, in our judgment, constitute obstructive conduct, had a nexus to a pending or contemplated proceeding,
and were done with corrupt intent, each of which, under the Department's principles of federal prosecution guiding charging decisions, would need to be proven beyond a reasonable doubt to establish an obstruction-of-justice offense.