Maybe they just wanted to create ambiguous circumstances under which Amy died, which would still throw suspicion on Dudley but not necessarily make it look like a murder. Maybe they felt that if they make it too obvious - bloody knife and all, the queen will know it was a set up, and they didn't want to take any chances by taking it too far. After all, if Dudley really did it, would he not try to make it look like an accident too, instead of a direct murder? There were rumors like that flying around anyway, before it happened. Also, they may have been afraid that the queen would never execute Dudley, so in a case like this it would have been "all or nothing". But if they kept it more subtle, it would still serve its purpose, no matter what, with Dudley being under suspicion for the rest of his life, and never being able to marry the queen - which after all would have been their main objective. And this is exactly how it worked out, so it seems a little too convenient in a lot of ways, unless it really was an coincidence.
To be honest, none of these scenarios make much sense, but IMO suicide is the most likely scenario, as they had originally thought, although it is still a little odd. But Amy after all did insist very adamantly to be left completely alone that day, why? Maybe she had brittle bones from her illness, as you said, and perhaps she was warned of this by her doctors, and perhaps she was very depressed and threw herself down the stairs deliberately, knowing that it would kill her...
It's a pity that there is no way to find out what really happened.