@ Tranquilty - There are no Forum rules, nor rules on that thread, that require proof or screenshots to be posted. Even a screenshot is not proof, as the screen that shows the trade value & who you are trading with appears before the final accept button is clicked and there is no way to know if the trade shown actually completed or was declined after the screenshot was taken.
If you believe that posted trades are inaccurate or false, then you are free to ignore them and not consider them when making your own calculations about prices.
There is no way for Forum Mods to investigate manipulation accusations. If you suspect there is manipulation happening, that should be reported to Jagex using the