In which case, there will more than likely never be an issue.

No worries if that's the case. However I note that CBF do state that the first body to chassis mounting at the front (i.e. the first one behind the front axle) has to be spring mounted, and I presume they mostly cater to vehicles for main highway driving.

How important is it that the first mounting is spring and not rigid?

I don't think there can ever be a definitive answer when building one-off vehicles. Much depends on intended use. Horsebox construction in the UK at least usually sees the habitation box (overcab luton included) flared into the vehicle cab and they don't seem to tear themselves apart in highway / getting-on-and-off-fields use. Builders seem to pay little attention to the concept of chassis twist. Maybe the extra heavy duty floors they use to support the weight of horses helps keep the whole structure rigid.

I suspect, though, that if they ever approached the limits of suspension in a cross axled manner then things could turn bad pretty quickly.