I played a game recently (my first game ever, and my opponent's first in years), and a rules dispute came up towards the end.

He had a large unit of Sebeki that had the left side of one model of my smaller Sebeki unit in the front 90 degree arc. He tried to charge into the side of my unit, but thanks to various spell/terrain movement modifiers, the only way he could contact my unit was touching the side of his unit's furthest right model into the side of my unit's furthest right model.

We decided to play it off as though he couldn't make the charge, as he couldn't bring his front to contact my unit's side, but were we mistaken?

In this case I think you were mistaken. The charging models need to make frontal contact with the model being charged.

Of course, as it was a friendly game at home then whatever you decided was correct for that game

Ah, just realized I had made a mistake in the original post (which is now fixed). We determined that he could not make the charge.

In which case, I think that you made the right call