Not true about the sword, Harry doesn't learn what the sword's purpose is until book seven. When Rufus Scrimgeour (who they ALSO cut out wtf) confiscates the sword Dumbledore left in his will, Harry still doesn't know at the time why he gave him that, and don't forget they bust their balls trying different ways to break the locket once they get their hands on it, and then one of the portraits mentions Dumbledore used the sword to break the ring. The sword isn't mentioned once in book six... or even five for that matter.
But yes, how the hell are they gonna get around not explaining the Horcruxes, that was important, Dumbledore theorizing and the memory of Riddle in that shop. Anyone who hasn't read the book would probably also wonder "okay, this ring apparently was a Horcrux Dumbledore destroyed... I guess I'll take their word for it". Also, his HAND! Where was his black hand, it's important as to why he let Snape kill him.