This is of course true for most expensive experiments. I can't afford a LHC, Space telescope, not even a small tokamak to test hot fusion. And the LHC produces so much data I can't even afford enough harddrives to store a copy. And even if I could, I'm not sure I have the knowledge to write a program to parse that data myself (or buy sufficient computer power to have it finished in my lifetime). Noone claimed you must me able to re-verify each and every experiment. And in many cases this is just simply impossible in practice. However, when the successor of the LHC will be built (they are designing some pulsed linear collider now in CERN, got a nice explaination of it when I visited last year) its results should not contradict the LHC results.
In CERN, this was partly solved by keeping the results of the 2 main detectors in LHC separate and just compare the end results. This should prevent matching the results voluntarily or involuntarily.