There is a surprisingly lengthy debate over this issue between the two gravediggers in Act 5, Scene 1 of Hamlet. Between them, they do essentially elucidate what has happened--the first gravedigger reiterates that those in power have ruled that Ophelia is to be buried in the proper fashion; the second gravedigger says Ophelia is being treated like a man to whom "the water come to him, and drown him, he drowns not himself" (as if her death were an accident) but that he feels "if this had not been a gentlewoman, she'd have been buried out o' Christian burial."
What he is indicating here is his own opinion that Ophelia's noble family has interceded on her behalf to have the coroner rule her death accidental. He himself does not believe this ruling at all and thinks political favor has been invoked. It is highly likely, given Polonius's position, that political favors were invoked, but the Shakespearean audience would recognize this debate. Because suicide was so poorly viewed at this time, all families, noble or otherwise, would sometimes go togreat lengths to try to conceal the manner of a family member's death. It may be likely that noble families were more often successful in having these deaths ruled "proper."
However, we could also ask the question of how much these gravediggers actually know about what happened in the circumstances of Ophelia's death. The play itself does not state for certain that she willingly drowns herself so much as she does not fight what she feels to be her fate. Because suicide was such a contentious issue, it also generated much gossip, and it is likely that some people who did indeed die by accident were gossiped about as if they had been suicides. Shakespeare could equally be highlighting the fact that more attention than is perhaps necessary is paid to this issue by onlookers whom it does not really concern.