The Shalom Bayis Of The Leviim In The Midbar

Someone asked me over Shabbos that in light of the fact that the מחנה לויה was אסור לבעל קרי - how were the Leviim were allowed to be משמש מטתם?

I searched and saw that the Meshech Chochma [Bamidbar] addresses the question and offers an answer. I further found [בעזרת השם ולהבדיל תוכנת אוצר החכמה] that Rav Chaim Knievsky Shlita answered that they went to underground tunnels [not only for the Arabs in Azza!]. Then they were tovel immediately and went up.

According to his chiddush, it was pointed out, you have to add three chiddushim - 1] Such tunnels existed 2] The tunnels didn't have קדושת מחנה לויה. Three]  They had a mikva down there as well.

Hmmmm.

Any other suggestions?