People laugh when we buy some players for too much money, rightfully so, but then we see those 'light heads' stating how 'we must pay a lot more since we're a big club'.
Real moves prove all of them wrong.
In regards to both Ozil and Sahin, I am pretty sure that many teams did contact Werder, Dortmund and the players agents but all of them wanted to do it silently. That's why all we heard about both of them is how Real is signing them, without hearing anything about other teams making a move.
In Sahin's case in particular, Dortmund didn't want to sell him so they never tried to build up his price, which was a set price anyway. Sahin's agent most probably contacted many teams and waited for the best offer, which turned out to be Real's.
I wouldn't bet that Juve didn't try to get Sahin. I'm sure many others did so too. But Juve and all the others who don't belong to the "richest" group stood no chances when Real got involved.