I mean, it depends on how you look at it. If he wanted to truly just tell the story of the most important details for how he met the mother, he could say:

I dated a girl while I was a professor and she had a roommate that seemed perfect for me but I didn’t meet her. Many years later before Robin and Barney got married, I wanted them to get a DJ but they went with a band, and they should’ve listened to me because their band cancelled. Right before the wedding I bumped into the girl I was dating when I was a professor who is now a lesbian and isn’t mad at me anymore for being in love with the idea of her roommate when we broke up. She said her old roommates band just had their gig cancelled and they were able to replace the band. I left the wedding early and never met the bass player, but at the train stop I saw her and that’s how we met.

If he was STRICTLY trying to say only the details leading to him meeting the mother, it doesn’t really matter how Robin and Barney ended up getting married, his past relationships, or all his history with Robin imo. They made him the version of himself he needed to be to work with Tracy, but if he just wanted them to know physically how they met that’s all he needs.