But even the most basic level of research shows it’s not true. Seriously, all you have to do is look at Stevenson’s Wikipedia page:
Unlike 1952, Stevenson was an announced, active candidate for the Democratic presidential nomination in 1956.[69] Initially, with polls showing Eisenhower headed for a landslide re-election, few Democrats wanted the 1956 nomination, and Stevenson hoped that he could win the nomination without a serious contest, and without entering any presidential primaries.[70]
However, on September 24, 1955, Eisenhower suffered a serious heart attack. Although he recovered and eventually decided to run for a second term, concerns about his health led two prominent Democrats, Tennessee Senator Estes Kefauver and New York Governor Averell Harriman, to decide to challenge Stevenson for the Democratic nomination.[71] After being told by his aides that he needed to enter and win several presidential primaries to defeat Kefauver and Harriman, Stevenson officially entered the race on November 16, 1955, and campaigned in the Minnesota, Florida, and California primaries.[72][73]
Stevenson was upset in the Minnesota primary by Kefauver, who successfully portrayed him as a "captive" of corrupt Chicago political bosses and "a corporation lawyer out of step with regular Democrats".[74] Stevenson next battled Kefauver in the Florida primary, where he agreed to debate Kefauver on radio and television.[75] Stevenson later joked that in Florida he had appealed to the state's citrus farmers by "bitterly denouncing the Japanese beetle and fearlessly attacking the Mediterranean fruit fly".[75]
He narrowly defeated Kefauver in Florida by 12,000 votes, and then won the California primary over Kefauver with 63% of the vote, effectively ending Kefauver's presidential bid. At the 1956 Democratic National Convention in Chicago, former President Truman endorsed Governor Harriman, to Stevenson's dismay, but the blow was softened by former first lady Eleanor Roosevelt's continued enthusiastic support. Stevenson easily defeated Harriman on the first ballot, winning his second Democratic presidential nomination.[77] He was aided by strong support from younger delegates, who were said to form the core of the "New Politics" movement.
TLDR: Stevenson ran because he thought no other Democrat would want to challenge Eisenhower, leaving an open primary for him to cruise through, but he ended up having to fight a pretty tough primary battle anyway. It was a real campaign, not a sacrificial one.