It is possible to physically create a 1:1 table pair, which is a pain in the toches to maintain. However, the conceptual design for relational tables is all about the keys. If a group of attributes (fields) depend exactly and ONLY on the same key they belong in the same table as that key because they are describing the thing selected by that key. Remember, that last statement is "for relational tables"!
Therefore, conceptually, the answer is NO, that design is not really conformant with theory for most situations. However, it is both possible and easily imagined that you can have two tables that APPEAR to justify a 1:1 relationship. Usually upon closer examination you find that the 2nd table is something different and you merely hadn't (yet) identified the difference so don't (yet) have the proper distinguishing attributes that allow for identifying the differences in the tables. Omitting the distinguishing properties so that you could create a 1:1 pair of tables is merely hiding the reality of the situation. For instance, consider your person ID number and the government ID card in your prior thread. When we dug into the situation we found that the card had renewal information that a person doesn't have, and therefore you actually had a 1:N relationship with the N-side being the various renewals and other administrative history of the card.
One of the reasons I said you could break the 1:1 rule is for security issues. In one particular U.S. Navy personnel database, we had a couple of 1:1 tables relating to personnel information. One of the two tables tracked "ordinary" data but the other table tracked data controlled by the USA Privacy Act, thus having different security requirements. This was an ORACLE back-end, not an Access back-end, so we could actually impose data-access restrictions selectively.
The other exception is one forced by mechanical limitations. If the REAL record would have had 300 fields in it and you were using an Access front end, there is a 255 field limit on queries. So you would break that long record up into at least three 1:1 parts, each part containing a subset of the real record. Then you could JOIN any two parts at once though you couldn't JOIN all three parts. However, the odds of a 300-field record being meaningful is rather low and therefore unlikely to be a reasonable situation.
I guess it is possible to come up with a contrived scenario that would SEEM to support a 1:1 table pair, but usually what happens is that you eventually recognize that there is something different about one of the tables that justifies the separation but ALSO makes the relationship to no longer be 1:1 - which invalidates the contrived scenario.
Does that help?