The isse at hand is whether or not Ophelia deserves a Christian burial in light of the rather suspicious circumstances of her death. If Ophelia willfully committed suicide, then she committed a murder (of self), and therefore committed a mortal sin which the Catholic Church would say precluded her from being buried in sanctified ground. Suicides where generally buried in a field or at a road-side -- someplace suggesting the lack of dignity of the act of suicide.
Because Ophelia drowned, the question is: did she drown herself or was it an accident? The gravedigger explains it as follows:
If the man go this water and drown himself it is, will he, nill he, he goes. Mark you that. But if the water come to him and drown him, he drowns not himself; argal, he that is not guilty of his own death shortens not his own life.
Because Ophelia shows clear signs of craziness and the description of her death suggests that she didn't try to save herself, she merely let herself sink, it is likely that she did, indeed, kill herself. But because her father was Polonius and she is close the king's family, Claudius probably intevened with the law so that Ophelia's death would be ruled an accident. This move would save her reputation and keep Laertes under Claudius's control. The loss of both his father and now his sister could drive Laertes over the edge, and Claudius needs him to fulfill their plan against Hamlet.