Reb Moshe zt”l’s psak mentioned above is remarkable for a different reason. His “proof” is that “no one has ever heard of such a psak”. He could easily have said that the chalitza is invalid, and this is the psak, and now you heard it. In other words, you married outside of your social circle and you have to suffer the consequences.
The point that Reb Moshe made is that such a psak would be inconceivable. So too with the Rabbeim’s psak in the OP; it is inconceivable.