I think it's a matter of logical extrapolation:
‘Nothing Kreacher did made any mark upon it,’ moaned the elf. ‘Kreacher tried everything, everything he knew, but nothing, nothing would work ... so many powerful spells upon the casing, Kreacher was sure the way to destroy it was to get inside it, but it would not open ... Kreacher punished himself, he tried again, he punished himself, he tried again. Kreacher failed to obey orders, Kreacher could not destroy the locket! And his mistress was mad with grief, because Master Regulus had disappeared, and Kreacher could not tell her what had happened, no, because Master
Regulus had f – f – forbidden him to tell any of the f – f – family what happened in the c – cave …’
Deathly Hallows - page 163 - Bloombury - chapter ten, Kreacher's Tale
Regulus had ordered Kreacher to destroy the locket; I'd wager that Regulus -- having grown up with Kreacher as his family's house-elf -- knew that house-elf magic is different from wizarding magic. Regulus was also the one who picked up on Voldemort's hints that he (Voldemort) had made at least one Horcrux -- Dumbledore said to Harry at one point during Half-Blood Prince that Voldemort had been so arrogant that he believed he could drop hints about Horcruxes and none of his Death Eaters would catch the clues: "I, who have gone farther down the road to immortality" (or somesuch -- I'm paraphrasing).
I would suggest that Regulus figured out that Voldemort was making Horcruxes, but Regulus did not know how to destroy a Horcrux. He may have thought that Kreacher's powerful house-elf magic, and the fact that a house-elf cannot disobey a direct order, would be enough to destroy the locket Horcrux.
Harry dragged his rucksack towards him and pulled out the fake Horcrux in which R.A.B.’s note was still folded.
‘“I have stolen the real Horcrux and intend to destroy it as soon as I can”,’ Harry read out.
Deathly Hallows - page 87 - Bloomsbury - chapter seven, The Ghoul in Pyjamas
It doesn't make a whole lot of sense that Regulus would not have known how to destroy a Horcrux -- and instructed Kreacher on how to do so, accordingly -- because in Deathly Hallows, Hermione reads to Ron and Harry about Horcruxes from the book Secrets of the Darkest Art, which explicitly lays out how to both make a Horcrux and how to destroy one. In the same chapter, The Ghoul in Pyjamas, Hermione explains how Dumbledore removed all books from the library having to do with Horcruxes, but she doesn't know if Dumbledore did this before or after he became Headmaster.
I think Dumbledore removed the books after he was headmaster, because Voldemort, while still Tom Riddle and a Hogwarts student, likely managed to get hold of Secrets of the Darkest Art and learn about Horcruxes (Note that when Tom Riddle talks to Slughorn about Horcruxes in Half-Blood Prince, he's not really interested in how to make a Horcrux -- this is a guise. He already knows how to make a Horcrux. What he's really after in his convo with Slughorn is what might happen if one splits one's soul seven times. Hermione confirms this, also in the chapter The Ghoul in Pyjamas.).
We know that neither Sirius nor Regulus were at Hogwarts at the same time as Tom Riddle, and that Tom Riddle had become Voldemort by the time the Black brothers became students at Hogwarts. Presumably, Dumbledore, who became headmaster in approximately 1957 (the first rise of Voldemort was in the 1970s) had removed all the books dealing with Horcruxes from the school library by the time Regulus was a student, so Secrets of the Darkest Art was most likely not available to him through school.
However, I can definitely imagine the Black family owning books on dark magic. Perhaps they owned a dark arts book that explained what a Horcrux is, but did not detail how to destroy one. It's possible Regulus learned what a Horcrux was from a family member or close family friend (or the like). These are the only circumstances I can put together from canon, and that would explain why Regulus knew what a Horcrux was, and was able to put together Voldemort's oblique hints and figure out that Voldemort was making at least one Horcrux, yet still didn't know how to destroy a Horcrux. His note, left in the fake locket Horcrux, says he would destroy the Horcrux "as soon as [he] can", yet he doesn't do it himself or right away. Nor does he give explicit instructions to Kreacher -- and house-elves require implicit instructions for almost everything -- really implies he didn't know how to destroy it.
So, coming back to Kreacher, the fact that his house-elf magic, which is more powerful than regular wizarding magic, failed to destroy the locket while it was closed would suggest that Kreacher logically concluded that the locket had to be opened in order for whatever it was inside to be destroyed (Regulus never told Kreacher the locket was a Horcrux; Kreacher didn't know he had been ordered to destroy part of the Dark Lord's soul.).
I almost think the real question at hand is Why didn't Regulus know how to destroy a Horcrux? Or, Did Regulus know how to destroy a Horcrux? I give you that if he did know how to destroy a Horcrux, it would have been basically impossible for him to get a hold of Basilisk venom. As a Slytherin, the Sword of Gryffindor would have never presented itself to Regulus and therefore couldn't have become impregnated with Basilisk venom as it did for Harry. However, as a Slytherin, a member of the dark-leaning Black family, and a follower of Voldemort, Fiendfyre should have been known to him. And if Crabbe, of all the idiotic lumps, could conjure Fiendfyre, then surely Regulus Black -- who Slughorn seemed glad to have taught and to have had in Slytherin House -- would have been able to conjure it as well.
I'm sorry this is so long, but I think it's a complex quesstion. I almost want to say it's perhaps a continuity issue.