BINARY operator not working properly

[Marco Nogueira]

I have this query:
SELECT 1 AS one FROM `products` WHERE `products`.`price` = BINARY 1.1 LIMIT 1;

That doesn't return the one row it should, but it works fine if I change it to :

SELECT 1 AS one FROM `products` WHERE BINARY `products`.`price` = 1.1 LIMIT 1;

Now I wonder, why?
From the docs (http://dev.mysql.com/doc/refman/5.1/en/charset-binary-op.html), we should prefer using the BINARY before the value (first statement), so it can use the index, and I assumed that this was a "good practice".

Can someone, please, point me towards the solution? Is this a bug?
(Ver 14.14 Distrib 5.1.54 by the way)