I don't have any documentation, but I've been flying A LOT for many years (last year flew 108 flights for a total over over 150,000 miles). What the parent comment above you is saying is true.
It is common knowledge among frequent flyers that you can get better prices sometimes if you're not signed in. For example, if you fly 100,000 miles a year with an airlines, they're pretty confident you're going to fly with them, so why not show you a slightly higher fare? The worst part: it works. I go to HipMunk sometimes and see a fare for $500 dollars less (on the same airline), but I still book through my preferred airlines, because the benefits are worth it for me: no hassle security, no hassle baggage (first on, first off), no hassle boarding, good chance of 1st class upgrade, etc.
The good news is that if you do find a lower fare on ITA (and pretty much only ITA), you can usually call the airlines and get that fare. Fares are bucketed into fixed "fare classes" so if there is availability in a cheap bucket, the airline MUST sell it to you.
The bad news for frequent flyers is that many benefits do not extend to these cheaper fare buckets. For example, if I want even a chance to be upgraded to business class for free on a transatlantic flight, I have to purchase one of the most expensive economy fare classes. Concrete example: I am flying to Israel in a couple months; for the cheap economy fare it was $1400, but for a chance at an upgrade it was $2,100. I took the $2,100 fare, because being in business to TLV is quite important to me.
Its unfortunate, but its how it is.