We know that the sword will only appear for true Gryffindors. But once it is there, couldn't it be used by everyone? Snape was able to hold and carry the sword to the Forest (and if he can hold it, he can use it). So why must Harry take it under conditions of need and valor? Snape could just have placed it before their tent for example, they would find it and be able to use it. The sword does not serve people as the elder wand does, if it is already there, lying in the floor, is it really necessary to do something brave in order to get it?
Comment from Jon Custer about magically showing up vs picking it up from the trash seems to be the critical point here.
What was important was that Harry and the gang believed that the sword came here magicaly.
If the sword appears in the situation needing valor. It means that the sword choose to be here.
So it's ok in this instance to find this ultra precious artefact lying around.
It's magic, so it's ok !
On the other hand, if that the sword pop up in front of the tent. It mean that someone put it there. So they will investigate, and they will distrust it.