Prateor's Grasp - Can Opponent Determine Taken Card Before Shuffle
The ruling was sorely mistaken.

406 Exile
406.3 Exiled cards are, by default, kept face up and may be examined by any player at any time. Cards “exiled face down” can’t be examined by any player except when instructions allow it. [...]

Your &quot;spirit of the card&quot; argument is very much relevant, as it would make the &quot;exile face down&quot; bit meaningless.
As for your opponent looking through his library: Nope, absolutely not. A library is a hidden zone that may also not be looked through unless an effect allows one to. This is very basic stuff.

401 Library
401.2. Each library must be kept in a single face-down pile. Players can’t look at or change the order of cards in a library.

If your judge really said exactly that &quot;a player may look at cards in one of his hidden zones as long as it doesn't take too much time&quot;, taken literally, would totally uproot the purpose of hidden zones, as it would allow me to, oh I don't know, look at the top 5 cards of my friggin' library, because, after all, that wouldn't take long, would it?
Ludicrous. People failing such basic concepts should not be judge.

I guess I understand where the judge is coming from. While your opponent shuffles, I guess it's ok for him to have a quick peek at his library, because he doesn't gain any information he is not privileged to. However, in this concrete situation, with an unknown card exiled, it still isn't ok, because it would give him an opportunity to circumvent 406.3 and part of the Praetor's Grasp effect. So you had every right to demand enforcement of 401.2 to the letter.