Earlier quoted context omitted.
I agree with you for the most part, but nearly all introductory courses must have content that is easily available online. Consider teaching students how to write a recursive method. What would their first assignment be? List length? "find length of list" Factorial? "factorial recursive" Fibonacci? "fibonacci recursive" GCD? "program gcd" There are only so many simple recursive procedures, and I guarantee nearly all…
It is trivial to create a simple recursive problem without saying anything that would be a Google-able search term. The problem may be solved, but the students won't know what to search for. For example have them write a program that solves the game of Nim, but don't tell them the name of the game they are solving. Instead call it "pick up pennies" or something like that. Now Google won't help.
However, there will be someone in the class who knows that "pick up pennies" is just the game of Nim, and will google it. Renaming makes it harder so fewer people will be able to cheat, but it doesn't make it impossible. (That said, it wouldn't be all that hard for the professor to create his own game which is similar to Nim in some respects, but different in others -- I believe this would be the best solution -- but unfortunately most professors would not put the time in to do this.)
This problem multiplies tenfold when you try to do it with math. (Integrate _____ -> WolframAlpha. Prove ______ -> Google.)