If Jeremy had actually killed anyone at all,,he'd have made sure that most valuables such as small items like jewellery would have been well pocketed,,as nobody would then have been the wiser as to what was in Junes' possession. Also,,it would have been a far easier task who to pinpoint if certain items had been missing ( such as what the relatives knew of )
No sign of a break-in----jewellery missing,,it WOULD then have made more sense to blame Jeremy,as regards greed. I'd have blamed him myself.
All " sellable " items still remained in-situ. Seems strange to me,,seeing as he knew how to steal !