Halacha depends on the facts of a situation. Generally, when one cannot know the exact facts, he is expected to assume that they are as usual (rov), or as they were when last checked (chazaka). When one knows the facts, can he deliberately cause himself not to know them? We seem to find contradictory rulings in various branches of halacha.
For example, one cannot take a non-kosher spoon identical to other, kosher spoons, and hide it among them (Shulchan Aruch, Yore Dea 99:6), causing himself not to know the facts.
Moreover, there are times when one must strive to ascertain the facts, which seems to be even stronger than a prohibition on causing himself to not know the facts. For example, even though "shehakol" works on any food b'diavad, one can't eat something, saying "shehakol", if he doesn't know what sort of food it is (e.g., Kitzur Shulchan Aruch 50:2): he must ascertain the facts if he can. Similarly, as DoubleAA notes in a comment, one is required (SA, Orach Chayim 8:9) to inspect tzitzis before donning their garment, so as to be sure they are kosher, again a requirement to ascertain facts.
However, one can hide a dairy spoon among pareve spoons, causing himself not to know the facts. (I can't cite this at the moment, but am pretty sure of it.)
Also, someone not in her shiv'a n'kiyim should wear colored clothes so as to hide any potential spotting (SA YD 190:10), causing herself not to know the facts.
Also, I seem to recall (but cannot find) that bes din, in interviewing witnesses to the new moon, would be deliberately cursory if they knew (by calculation) the correct date, so as not to find out the witnesses were lying, again causing themselves not to know the facts.
So my question is: Are there specific parameters for when we say one can deliberately not know the facts? What is it about the first case I give, and others like it, that distinguishes it from the latter ones, and others like them?