You make the assumption that people are smart and don't do foolish things.
That is manifestly incorrect.
Just take a look at how many people just scatter their personal information all over the damn internet without even thinking about it. Even after being warned repeatedly not to do so.
Hell, I have to stop my dad, who has been in the computer industry for decades, from clicking on strange interweb pop-ups.
Now, I might limit the amount and type of legwork obtainable with just Data Search, but they should be able to get some stuff.
Then I will make my evil GM laugh as their incomplete Data Search legwork leads them to completely wrong conclusions about their current run and results in all sort of trouble for them.
I almost never tell my players, "No, you can't do that". They have, however, learned that some stuff carries consequences, and if the GM is smiling it's already too late.
-k