I am going to state what transpired in our little conversation as an answer for posterity. The answer also includes bits and pieces of advice I received elsewhere, so feel free to comment if you consider some of it incorrect.
1. There are no tagging differences among polygons with different topology: both closed way polygons and multipolygons can we tagged with either place=\*, or boundary=administrative, or both. The difference is in what these polygons represent, not how they are drawn.
2. Both place=\* and boundary=administrative schemas are in use, neither is outdated or deprecated, or superior to the other. They neither supplant nor conflict with each other. In some countries and states they are complementary, in others they can be seen as redundant. That is okay.
3. If a polygon defines the boundary of a settlement, it gets a place=\* tag and related tags. If a polygon represents an administrative boundary, it gets a boundary=administrative + admin\_level=\* tags. If the administrative boundary coincides with the settlement, then it gets both sets of tags. However, some purists recommend even in this case tagging the closed way polygon as place=* while at the same time creating a boundary relation where this same way is added as the sole outer member, and tagging the relation as boundary=administrative + admin\_level, etc. I personally consider this excessive, especially given that Nominatim knows about the logical difference between place and admin boundary and will create two objects while indexing this same а polygon with both sets of tags.
4. If an administrative boundary is shared by two or more entities, it should be broken up into segments, each of which should be added to two or more boundary relations. The way segments in this case should only be tagged boundary=administrative + admin_level=\* with no name. If the admin boundary is the same as settlement boundary AND all boundaries are shared (this was my initial question) then each place gets represented as a multipolyogn (or boundary relation, which is synonymous), which gets tagged with BOTH place and admin tags, as described in 3. The aforementioned purists would have us create TWO multipolygons for each entity in this case: one tagged as place=\*, the other as administrative. Each way segment would then belong to a FOUR relation. That is just too much.
5. All relations must have a type tag. (Closed way polygons don't.) A boundary relation can be tagged either type=boundary or type=multipolygon. I feel a little uneasy about the fact that [wiki][1] leaves plenty of ambiguity (or is it ambivalence?) on this point. This is especially unfortunate because the leading mappers, in contrast, have a very strong personal opinion in favor of one or the other. Fortunately, software (as wiki prescribes) supports both.
[1]: http://wiki.openstreetmap.org/wiki/Relation:boundary