It is not just limiting to UA cannot see SQ inventory issue. A lot are in play here.

I remember I had LH flight from LHR tranit in FRA to SIN. Flight was cancelled. SQ has wide open business class cabins on LHR-SIN and FRA-SIN, but LH could not book me.They couldn't see the inventory.
They booked me on BA instead.

Good that OP managed to rebooked onto NH.
I guess there are differences between JV partners verus just alliance partners.