I don't see any timing issue, unless players are limited to spying via an Obfuscate Code.
I find little difference between a request for information via spying and a request for information via investigation into a PC's background. I see no burden in asking the target PC's player for that information, and, if there is an impasse, seeking staff intervention to, as you put it, make everyone's IC lives a little more interesting.
We want to be able to trust staff to handle conflicts, but if we cannot trust fellow players to be trustworthy and cooperative then we have other, deeper issues to contend with.