Of course, they can cheat... especially if you don't check, but I'm almost 100% sure that you can check the entire economy and replay 99% of the battles using daily saves... otherwise, you can request a description of the battle (that could not be repeated)... and even in that case, you can determine whether this battle is real or not...
Alexander, you've already started talking about the fact that they can only attempt to cheat, and not actually commit the act (i.e., without moments where the cheat itself could be noticed). Of course, it's unlikely that you can select all the battles yourself (like morale, luck, and all that...), but what if you use such a program to add 2-3 creatures (a relatively small number) and win the battle with their help, citing morale as the reason? Is there a 100% way to verify this example, or am I missing something...? :)