Certainly, but if the victims in the case don't feel that they've been raped, perhaps that's more important than the technicalities of what the State may or may not do.
If rape was defined just be whether or not the victim felt it was rape, the victim could change their mind after-the-fact and Assange would go from not-rapist to rapist (and possibly to not-rapist again) based on not on their own actions by based on someone's feelings of guilt, anger, intimidation, or forgiveness a month from the act. This only makes any sense if you view crimes as being individual injuries to one person. But that isn't how criminal law works. If I walk up to you in the middle of a hackathon and stab you in the forearm, I have indeed harmed you and you can sue me for damages in civil court. However, I have also harmed society, specifically that part of society where people assume they can go to hackathon a without being stabbed.
A great source to learn about the fundamentals of criminal law and criminal procedure is this page maintained by a former prosecutor who now works as s defense attorney in NYC. http://lawcomic.net/guide/?page_id=5
All of this should also apply on a smaller scale to communities with Codes of Conduct: http://thebias.com/2015/08/12/take-responsibility-for-handli...
EDIT: I am not a lawyer and comments from a random person on the Internet do not establish an a attourney-client relationship. For actual advice about criminal or international law, please contact Nathan Burney, an actual lawyer who also happens to maintain the illustrated educational resource that I've linked to and I think is fantastic.
Plus your stabbing example doesn't explain anything since you would have indeed physically harmed someone which is against the law in most jurisdictions. Considering your rape/not-rape example, a better example is that you would be arrested for thinking about stabbing someone in the arm as you are placing your hand on that arm.
If I were on the jury for either of these examples, supposed victim says no crime committed and the only evidence is the accusation from the state? There's no way you could convince me to vote to convict.
If the victim says that the accused did X, Y, and then Z, that is a statement of fact about what happened. If the victim then says that he doesn't think that X, Y, and Z constitute a crime, that is a statement about the law..which might just be incorrect.
* except for strict liability crimes like speeding
However, if the "victim" says there was no rape, and has never said so, then the whole premise, including both the intent and the act, is unseated.
Disclaimer: I am no lawyer, and do not know much about this specific case. These are just my intuitions about rape laws. I also believe that if the laws, in fact, are much different from these ideas in spirit, they are SORELY off-base.
I am simply saying that in a criminal case if the only evidence presented is the accusation of the prosecution, especially if the supposed victim proclaims they are not a victim of the alleged crime, then I will find it hard to convict if I'm on that jury. Regardless of what the law says or the alleged intent of the accused.
In cases that any law can provide a conviction with no evidence other than an accusation from the state then that's an extremely bad law and should be stricken.
That sounds like an interesting theory on Crime and Punishment.
Edit: If you feel I've misunderstood the parent comment, please provide a better explanation.
This concept is called "mens rea" or "guilty mind". A statute for each crime should define what type of mens rea it requires. As an example, generally murder requires an intent to kill or seriously injure someone. Manslaughter only requires a reckless disregard for whether or not you've harmed someone. However, some crimes do not have a mens rea requirement. They are usually minor, like speeding.
For a better explanation of mens rea, see this part of the linked site: http://lawcomic.net/guide/?p=173
EDIT: For an interesting example of when the mens rea requirements for a crime are unclear, see Elonis v. US: a free speech case involving intimidating speech posted to Facebook. http://www.scotusblog.com/case-files/cases/elonis-v-united-s...
For instance, murder requires both intent and action but manslaughter only requires action. Which leads to the canonical law school example of a hit man who shoots his victim with the intent to kill him but the victim does not die. Mistakenly thinking the victim is dead, the hitman leaves the body in a deserted spot in the woods whereupon the victim finally dies of exposure. The hitman technically did not commit murder because when he shot the victim, he intended to kill him but did not actually succeed. However, when he did finally kill the victim (by leaving him out to die of exposure), he had no intention of killing the victim (because the hitman thought the victim was already dead).
Of course, this is all theoretical and if you did try to pull off a crime by manipulating mens and actus rea, you would find prosecutors very creative in finding ways to throw the book at you.