If they think that the NUA has to be done first and they don't do it, there's a good chance that they will not report an NUA distribution and without that reporting it will likely be difficult to get the IRS to accept that there was a valid distribution of NUA. There will be no record on Forms 1099-R of the split between basis and NUA.
I don't understand why you would not just do the NUA distribution first the way they want since doing so would make no taxable difference to you that I can see (unless you will be acquiring more company shares in the meantime, but it's extremely likely that there would not be sufficient appreciation on those newly acquired shares to make NUA treatment particularly worthwhile on those shares).
