Some objects are clearly not derived from the archaeological record of England and Wales at all but are likely to be modern imports from another country altogether. While a proportion of these were perhaps lost by a modern collector or discarded by heirs unaware of their value (I know of an ancient Egyptian ushabti that now lies buried somewhere in a local landfill), some of them are likely to have been deliberately 'planted' as a joke or their findspot fabricated to enhance their resale price on eBay (a PAS record suggesting a British find raises financial value considerably). It is not difficult to see how the PAS database could also be used to launder foreign artefacts lacking a licit provenance.
I know little about coins so I tested the PAS results myself with a search for 'lamp', an artefact I am more familiar with. Roman lamps are a relatively rare find in Britain and the search took little time to go through. One of the Roman lamps was recorded as a "chance find during metal detecting" in Essex. That chance find would be more credible if the lamp was not a Syro-Palestinian type (Kennedy Type 5) found almost exclusively in the Levant and not brought into Britain as popular tourist souvenirs until modern times.
Another lamp, also described as "Roman", is recorded as having been found in Kent and only "identified from photograph". In fact, the lamp is not Roman at all; it was made during the Hellenistic period (more precisely the 3rd century BC) in the Eastern Mediterranean. While nothing is impossible, it is extremely unlikely that it ever formed part of Britain's ancient archaeology.
At any rate, that's just a quick glance at the limited number of Roman lamps recorded. I have no idea how many, if any, of the metal finds (buckles, fibulae, keys, coins, etc.) were actually modern imports from the Balkans and elsewhere. From what I've seen so far, my confidence in all of them really being found in Britain is not high.
The PAS system is often touted as a perfect panacea to unrecorded looting - and a model for other countries to follow. To be fair, I suspect it was only ever envisaged as a pragmatic compromise, a form of 'damage limitation' to appease the metal detecting lobby, and it also works well for genuinely chance finds. It could be argued that without it the situation would be worse and no finds recorded at all. But sadly, the PAS is inherently open to abuse.
What serious scholar can rely on the PAS to compile studies when so many of its records are likely to be polluted with false claims? Is the scholar expected to take pot luck, perhaps basing the study on the sheer number of finds in one location and desperately hoping that some laundering dealer didn't pretend to have found a dozen Bulgarian brooches in a small area? Or realistically, in many cases where accurate data is a must, is the whole system too flawed to be reliable enough for practical use?
If the PAS really is ever adopted as a model for other countries to follow, perhaps we can all look forward to some truly unexpected delights: a Ban Chiang jar discovered in Guatemala or a Haida totem pole turning up in Egypt. I may be exaggerating but personally, in the meantime, I would treat any study or survey based on it with a caveat the size of Stonehenge. At least we know Stonehenge really was found where it was purported to have been found. And I feel safer classifying that as "Certain".