The investigations were the court cases, all of which failed to make a case for a stolen election. Burden of proof was on Trump's lawyers; they failed to shoulder it successfully, repeatedly.
When two parties are in a discussion and one makes a claim that the other disputes, the one who makes the claim typically has a burden of proof to justify or substantiate that claim especially when it challenges a perceived status quo.
[1] This is also stated in Hitchens's razor, which declares that "what may be asserted without evidence, may be dismissed without evidence." Carl Sagan proposed a related criterion – "extraordinary claims require extraordinary evidence" – which is known as the Sagan standard.[2]
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