Is there ever a time where using a database 1:1 relationship makes sense?
A 1:1 relationship typically indicates that you have partitioned a larger entity for some reason. Often it is because of performance reasons in the physical schema, but it can happen in the logic side as well if a large chunk of the data is expected to be "unknown" at the same time (in which case you have a 1:0 or 1:1, but no more).
As an example of a logical partition: you have data about an employee, but there is a larger set of data that needs to be collected, if and only if they select to have health coverage. I would keep the demographic data regarding health coverage in a different table to both give easier security partitioning and to avoid hauling that data around in queries unrelated to insurance.
An example of a physical partition would be the same data being hosted on multiple servers. I may keep the health coverage demographic data in another state (where the HR office is, for example) and the primary database may only link to it via a linked server... avoiding replicating sensitive data to other locations, yet making it available for (assuming here rare) queries that need it.
Physical partitioning can be useful whenever you have queries that need consistent subsets of a larger entity.
One reason is database efficiency. Having a 1:1 relationship allows you to split up the fields which will be affected during a row/table lock. If table A has a ton of updates and table b has a ton of reads (or has a ton of updates from another application), then table A's locking won't affect what's going on in table B.
Others bring up a good point. Security can also be a good reason depending on how applications etc. are hitting the system. I would tend to take a different approach, but it can be an easy way of restricting access to certain data. It's really easy to just deny access to a certain table in a pinch.
Sparseness. The data relationship may be technically 1:1, but corresponding rows don't have to exist for every row. So if you have twenty million rows and there's some set of values that only exists for 0.5% of them, the space savings are vast if you push those columns out into a table that can be sparsely populated.