I haven't read the House of M Cap tie-ins, but I'm told his life was pretty sad at that point.
No more so than any other octogenarian non-mutant.
And Wolverine's desire wasn't for a specific incident to be changed, it was for something about himself to be different.
And the only reason to do it the way she did was because she was giving him EXACTLY what he wanted.
If it was just 'change something and let things play out' he'd have been given his general wish ('I want to know my past') without creating a window to undo the universe.
But that's not what she was doing - she was giving everyone who was there exactly what they wanted. So she let Wolverine remember his REAL history, instead of creating a new history and letting him remember that.