JMO, but I don't think this statement MMQC said the BF/F made means "she took off with the ring." For me, "I gave her a really expensive ring" translates to "I was good to her, I valued her, I made a promise and put money where my mouth was." I hear it as him trying to understand why she would leave that behind. And in combination with "and she takes off," I hear it as pain. This is why I have always suspected a breakup that night (which would also explain how he had the ring).
I am not sure he would have had any reason to tell the Ls about the ring if that happened. If, for example, SL broke up with him, since it involved breaking an engagement (a public commitment that involves families in a relationship), he might've have thought she talked about it to them first, that they were in on it.
We don't really even know why he went there that night -- did he go there to say "your daughter's missing"? Or did he go to say, "Is Sylvia back yet? I really need to talk to her?" If the latter, it might have been followed by "We thought she was with you!" Either way, the same story would come out.