Except that if you are rolling against other people your odds are the chance the item will drop * the odds you will win the roll. As soon as the other person that wants the staff wins the roll then your overall chances each week go up because you're no longer reducing your odds by another roll.
In the LFR system each week you run changes the odds you will win something by the random class makeup that you get. You might be the only shield wearer in the group one week, so if a shield drops you would have a 100% chance of winning it, but then the next week there might be 10 people who all want that shield for some reason or another, reducing your odds of getting it by 91% (1-(11/100)).
Now all of this is assuming the OLD RF system. Under the new system the class makeup of the raid does not matter, and what you say is true, each week your odds of getting the loot are the exact same from one week to the next. Overtime, your odds of getting it do go up because you're drawing multiple times from the same hat, but you are correct than any individual week has the exact same odds as the week before it and the week after it.
As much as it begrudges me to say this, Toypop is correct that a fixed roster system increases your odds to get an item over time because competition for that item decreases. That's not to say that the odds of that item dropping increases over time, these are very distinctly different things. The current LFR system does not have a way to increase the odds over time due to not having to compete with people once they get it like fixed rosters do.
The question is: is this a bad thing? I would argue no because it keeps people coming back to LFR, and once they do get stuff on their main/main spec it allows them to then queue as offspec and get on alts etc. It keeps queue times low and increases interest in LFR. But there has to be some sort of brightline on the odds of winning a piece of gear on any given fight.