I realize the statement itself is about current events, but my question is for all of American history, so I hope this is allowed. Right off the top of my head, I can think of George Wallace in 1968, Teddy Roosevelt in the Progressive Party, and the 1800 election in which Jefferson and Aaron Burr tied for first and Adams came in third. Do these examples not disprove the claim about the current election? Are there any other examples that disprove the claim?
There have been many third party candidates appearing on the ballot throughout American history. The question itself is particularly difficult to answer since only elections since 1960 have even HAD 50 states (remember Alaska and Hawaii were not admitted until 1959!)
Besides the problem of defining "third party" candidate (there have been multiple third parties such as the "Independents", Socialists, Prohibition and People's Prohibition parties and more...) there have also been candidates and indeed entire elections without parties. Remember that the very concept of parties wasn't really something the framers baked into the constitution.
You don't have to go back very far for evidence of a major third party candidate being not only on the ballot but an (arguably) strong contender. As recently as 1992, a candidate (Ross Perot) not only appeared on the ballot in all 50 states but received nearly 20% of the popular vote.
(Contemporaneous article about the election of 1992 which might give more context - published two days after the election)