One thing I do not do is leave a player hanging when I ask them for an explanation of their approach. Especially with non cut and dried actions like investigations and the like. I do not ask professional PCs to roll for basic competancy in a crime scene investigation, for example, unless for some reason there's a strong chance they might miss something (active interference, a professional cover up, they've been affected by something else that might impair them). Yes, I respect when people have social skills that they've purchased rather than just bullshitting through them.
I favor those PCs myself!
However, if they want to check for /more/ than their level of competency, or outside of the box thinking (and certain PCs want to do that all the time, because they may not fit the stereotypical mold but would still like to take a chance to find something), if they want a check of "I have this nuts idea, could I make it work," and it's something that I wouldn't usually think would occur but it's not totally impossible, but unusual--then I feel that they should be allowed to roll.
Also, and this is usually something that happens in group scenes, there will be someone who says "I can't do anything" because they don't have the precise Investigation skill. Will they be able to uncover the same kind or perhaps quality info as the person who does? No--but they can retrieve different info, depending upon the scene and if the investigator shares that info within the party, or clarify it, with occult, empathy, science, medicine, ect.
I find a ST who just says "tell me how" to be just as annoying as the ones that say "gimme a roll. Oh, you don't have the exact stat+skill I am looking for/used to? Nah sorry, you're out of luck." I have a gut-level aversion to making people play "guess what the ST is thinking to solve things" games. Not fun for me. Though if someone does enjoy that type of scene (which there's nothing wrong with), then probably our styles aren't going to mesh. If someone was struggling with that, I'd adapt for them. That's part of the role of a GM, IMO, you're responsible for the group enjoyment but also the /individual/ enjoyment of the players (unless they are being Brat Princesses Me First ME ME ME Only people). This may also be why for real STing scenes I prefer groups of 5 or less, so that I can give adequate personal attention to each person and keep things moving in a timely manner.