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.
So, and correct me if I am wrong, you don't think a little old fashioned nepotism happened like it does in pretty much every major industry?
One way to look at it is that if IBM considered licensing MS-DOS and CP/M to be equivalent, which is to say either one would serve there purposes. Then I can easily see the Chairman of IBM putting a finger on the scale to swing it toward Ms. Gates son. It's like a two-fer[1], IBM is going to do a deal anyway and they figure either OS would work, and he gets a 'favor' point from a fellow board member who he might someday need their vote on a board decision down the road. Politics at that level is all about the banking of favors and opportunistically cashing them in.
[1] "Two for one" -- two desirable outcomes from a single action.
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.