The system, administered by C[r]apita, does not log a disproved link... so we get:

DfE: "Hello, are you dead or is our wrong data match from last time still wrong?"

The repeated asking of the same question is them covering up a data quality problem!

Isn't this really a process problem (i.e. a missed requirement), so that after the first instance of a queried match (for whatever reason), the unrelated death record (which will have some kind of unique document identifier or can have one derived from the information on it and date of issue) can be excluded from being matched against the subject user? (As realistically you could have 2 people with same name and DOB, it seems like the issue here is not data quality.)

It sounds like nobody created a requirement in the design stage for the ability to say "I've checked this, it's not the same person, don't flag this same death entry again". That's maybe not something envisaged at requirements time, but the need for it now becomes apparent.