Earlier quoted context omitted.
In particular, his mother – Mary Maxwell Gates – was on the United Way board along with IBM’s chairman John Opel and reportedly discussed her son’s company with Opel a few weeks before they made the decision to license MS-DOS. https://www.nytimes.com/1994/06/11/obituaries/mary-gates-64-...
There's little doubt that Ms Gates suggested that IBM look into Bill Gates, but I seriously doubt that IBM made the major business decision to contract with Gates because of his mother's suggestion.
None of us know what was said but I have no reason to doubt it based on the reports of his subsequent conversations with lower-level IBM executives. It probably didn’t seem like an especially consequential decision both because neither Gates nor Kildall were especially proven at that time by the standards of a Goliath like IBM and the mainframe guys were notoriously dismissive of PCs (Opel came up through S/360). I’ve seen enough nepotism not to question the plausibility but it’s especially easy to imagine people high up the management ladder at the biggest mainframe manufacturer thinking it didn’t really matter which of the toy computer operating system vendors they picked. I didn’t work in that world then (that was my dad’s generation) but even in the mid-90s when I started working in tech it was not uncommon to find mainframe people who were dismissive of PC or Unix systems as non-serious.