I think some people who are in open relationships of various sorts would handle it the way he did. Some amount of women are at least willing to tolerate a one-sided open relationship so long as it does not result in public humiliation. Most people in an open relationship, either partially or fully open, do not publicly advertise it as it's non-conventional.

I thought I covered the privacy angle well enough; once it's exposed, admitting it's cheating seems far worse to me than admitting it's an open relationship.

Cheating may be more conventional, but it's almost universally considered immoral.