Honestly I gave it a good search on that site and could not find anything to what you claim. What I did find right away on the opening page was this as follows

Honestly I gave it a good search on that site and could not find anything to what you claim. What I did find right away on the opening page was this as follows "These five treaties deal with issues such as the non-appropriation of outer space by any one country, arms control, the freedom of exploration, liability for damage caused by space objects, the safety and rescue of spacecraft and astronauts, the prevention of harmful interference with space activities and the environment, the notification and registration of space activities, scientific investigation and the exploitation of natural resources in outer space and the settlement of disputes. Each of the treaties stresses the notion that outer space, the activities carried out in outer space and whatever benefits might be accrued from outer space should be devoted to enhancing the well-being of all countries and humankind, with an emphasis on promoting international cooperation." To me that last part is what I notice. Should be devoted to enhancing the well being of all countries and humankind, with emphasis on promoting international cooperation. So how would spying do any of that? It is more likely to get the other country angry and not cooperate. If there is relevant text that shows spying is actually legal please do show it, I am not saying you are incorrect but I am having a hard time verifying your claim. Do you have a direct source that spells it out? Again, thanks.