The odd thing (from an Access point of view) is that the row, to me, is identified by the condition.

Essentially what I was doing was used some VBA on Access to run this SQL on one of the tables:

"DELETE from tblScores WHERE VolunteerID='A1' AND NoWeek=3"

on a table tblScores having a structure like this:

VolunteerID | NoWeek | Score

A1 1 3

A1 2 5

A1 3 0

A2 1 11

........... etc

so the condition "WHERE VolunteerID='A1' AND NoWeek=3" only identifies one record in Access (but, oddly enough, SSIS rejects this). That's odd to me, but after adding the ID column it worked perfectly.