Is @@ROWCOUNT after UPDATE reliably a measure of *matching* rows?

To expand on xacinay's answer because he is correct.

You have 3 rows changed and therefore @@ROWCOUNT is accurate. The SQL Server changes all rows, it does not verify that a value is in fact different before changing it, as that would require a lot of overhead on update commands. Just imagining having to check a VARCHAR(MAX) for whether the value was actually changed or not.

The easiest way to illustrate this is to actually change yor UPDATE query to something like this:

UPDATE [Foo]  SET [b] = 1
OUTPUT INSERTED.b
WHERE [a] = 1

It will output 3 rows of INSERTED which is the 'pseudo' table that holds the new values for a given update/insert command. That the value in fact is already b = 1 in one instance does not matter.

If you want that to matter you'll need to include it in your WHERE clause:

UPDATE [Foo]  SET [b] = 1
WHERE [a] = 1 AND [b] <> 1
SELECT @@ROWCOUNT

Alternatively, and as a more general way of doing this check, you can make a trigger and compare the values/fields in the DELETED table with the values in the INSERTED table and use that as foundation for whether a row is actually 'changed'.

So - 3 is the accurate number as you have updated 3 rows because 3 rows were touched by [a] = 1

The documentation for @@ROWCOUNT is telling you the truth because 3 rows would be reliably affected as opposed to MySQL's ROW_COUNT().

not 2 (the number of rows modified by the UPDATE — one of the three rows already had the value 1 for b).

For UPDATE it's not important if the new and previous values are identical. It simply does what its told to: finds data source, filters rows according to provided condition, and applies 'set' changes to filtered rows.

That's the way SQL Server works without any reservations. MySQL may work different. A row counting procedure is not a part of the SQL standard. So, you have to look before you leap for those kinds of artefacts every time you switch from one RDBMS to another.

Some triggers to see actual update behaviour:

CREATE TRIGGER [dbo].[trgFooForUpd]
ON [dbo].[Foo]
FOR UPDATE 
AS begin declare @id int;
      select @id = [a] from INSERTED;
      select * from INSERTED; end;
GO
CREATE TRIGGER [dbo].[trgFooAfterUpd]
ON [dbo].[Foo]
AFTER UPDATE 
AS print 'update done for ' + cast(coalesce( @@ROWCOUNT, -1) as varchar )+'rows'