Edit: For the down voter: I searched around and found a discussion of the puzzle [1]. Please go ahead and read it.
[1] http://books.google.de/books?id=415loiMd_c0C&lpg=PP1&...
Maybe they meant "constant additional space". Or constant space for the data you are using in addition to the space required for the inputs.
That however tends to go against the main principles of complexity theory and O-notation. The main principle of O notation is that you mostly care on how things grow as n becomes large. Thus, constant terms should be deleted if you have a linear term. In other words, if you have something that adds constant space to linear space, you get linear space. Thus, if you already have something that requires linear space, and have to add something else to it, it is not that important (for complexity theory purposes) if the second thing is in constant space, or log space or even linear space, as long as it is smaller or equal to linear space.