Where I think we are missing the point is that Anchoress is saying that only older entries will have the 1/1 relationship. I.e. this is clearly an historical segment of the table.
If the following statement is true, then there is no violation and no problem in what is being proposed here.
1. The entries in the table at the time of the split have some extra data in the "supplemental" fields being moved to another place.
2. Newer entries in the table after the split will never have the extra data.
If this is true, then technically this isn't a real 1/1 relationship, it is a 1/many case because with respect to the newer entries, the historical table is SPARSE. It is not fully populated. In hard fact, for newer entries, that second table might as well not exist.
The relationship could legitimately be declared 1/many without a problem in any case. Just remember that INNER JOIN operations based on the newer table will not return records entered after the split, but an OUTER JOIN would do so. And that is true regardless of which table is the left side of the join and regardless of whether the relationship was declared 1/1 or 1/many.
Anchoress, the reason you have encountered flak from some of the members here is that a 1/1 key with one table being sparsely populated leads to issues of normalization from a purist's standpoint.
In "purely" normalized tables, the PK for a table uniquely identifies the record and all data in the record are selected by and depend on only the PK. I.e. the selection rules are bi-directional in their implication.
If there is a second table with the same key, the "purity" issue is that now you have data selected by the PK - and it is the same PK - but there is an implication of impurity because there exists data depending on an implied value - the date of entry of that record - which is NOT the PK.
That is, existence of the matching record in the history table now depends on something that isn't a PK. This is a violation of normalization rules, generally speaking. While you can certainly make such a database work, there is a taint on it that makes the underlying set theory questionable.
As a pragmatist, I would say go ahead and do it, but recognize that to use the tables together you will need to be very careful about the JOIN clauses needed for the operation. Only an OUTER join can fully rejoin the two parts correctly - and that induces good odds of having nulls in fields for which the OUTER JOIN found no matches. So you just escalated the cost of all future programming. (Which might be an argument that works when no other argument could be effective.)
Also you need to be aware that the FIRST TIME the bosses want to edit anything in the historical table, they violated their own rules. Make it clear that you intend to make that table read-only, to stay that way at least until two full days AFTER Hell freezes over. If they object, then tell them that the tables cannot be safely split if they still intend to edit anything. Send 'em my way. I'll explain their problems to them in short sentences.