Ancient artefacts

Visiting an antiques centre between Perth and Dundee yesterday, I was interested to see a cabinet given over to Ancient art. I was particularly attracted to a small Greek arrowhead, apparently dating from between the 5th and 8th Century BC. However, two things put me off. Firstly, the green patina suggested that it might be bronze, which would be suggestive of it being even older. Secondly, the Greeks were not renowned for being archers, they were spear chuckers. So, although it was interesting and affordable there was just something barbarian and un-Greek about it. Much more interesting, and correspondingly more expensive, was a short Persian stabbing sword, apparently dating from the 12th C BC. There wasn't any info on provenance and, whilst the dealer is a highly reputable organisation, I was left with the nagging feeling that these pieces ought to be in a museum somewhere or was there a good reason why they weren't?