I am also very puzzled as to why the NH, which must have been under construction for at least a year and is part of a wider care organisation, had not sorted out its relationship with SSD a long time ago.
In fact, a few weeks ago I had a similar problem with the health authority, who has sent me a letter saying they would pay £167 pw if OH went into nursing care; but then rescinded it as they were not familiar with the home and had no contract with it. That did get sorted with the home saying they would sort that out in the fullness of time; but in the meantime they would charge me as if health were chipping in their bit.
Really and truly you couldn't make all this up. Thank god I am not 90 and trying to cope with all this.