Error message "The row value(s)... alter multiple rows"

The full text of the error message is following:

"No row was not updated.
The data in row [number] was not committed.
The row value(s) updated or deleted either do not make the row unique or they alter multiple rows ([number] rows)."
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How it happened. I received this error message (and, indeed, was not able to commit any updates) when I was trying to change a value through the 'OPEN TABLE' option of SSMS. I saw that I am able to change values in some rows, but other give me this message. How could I alter multiple rows if, while working directly in the open table, you can only update 1 value in 1 row at a time? And, of course, T-SQL statement was allowing to update any values with no error messages.
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Explanation. It could be, indeed, that you have several rows with all the same values. One of the cases - you've recently dropped an identity field. Another case - you've just made changes to a row that turned it into a duplicate of another row. It is allowed, however, this row immediately turns into a read-only (it has a lighter grey color than other rows), and now, if you try to update its duplicate - you get this error message.
Workaround. There are cases when you want to make some hand-made changes directly in the table. If the situation of a non-uniqueness could occur, create a new identity field - then do whatever updates you need - then drop the new identity field.
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Additional observations. The same can happened if there are constrains that tie a table with other tables, although I did not investigate this case too far.