I completed the Orphan Trail and found that parish records and persons in the various parish record offices were extremely helpful. I invariably added the parish when records listed locations for births, marriages and in some cases burials. This is particularly relevant to 17th & 18th century records. All of my trail work was done in Cornwall and a prior answer mentioned how awesome Cornwall is relevant to their records.
As genealogists, it is incumbent on us to provide as much information as possible when developing and sourcing profiles. There are circumstances in which the parish may not be in the geographic region. Did they marry in the geographic region, then settle in the parish? Were they baptized in the parish then move to a surrounding region. In these cases, we should list the parish and mention in the biography the possibility of a move to the surrounding region.
In the case of 17th century Cornwall, in addition to finding christening, marriage and on occasion burial records, the parish records office made available the history of the time (e.g. the English Civil War ca. 1642) and listed members who had to take oaths to the Protestant church. There were names of my profiles who took that oath. This information was included in the profile (more evidence that the person being worked on is the actual person) along with the URL that provided this information.
The England Group and the Orphan Trail provide and support tremendous learning opportunities for the subtle ways in which sourcing is done in England. For those of us in the U.S., who are working on families who immigrated from England in the early 1600s, we can see how English Common Law influenced our birth, death, marriage and probate(!) records. I revisited my 5X GGF's probate record from 1759 last night and recognized the similarities to some of the wills I read (including personal and real property listed in BPS) doing my Orphan Trail in the 18th century.
Bottom line, I believe parish information should be included if parishes and parish records are so recognized. If need be, perhaps the England Group leadership can add a codicil to their documentation to incorporate use of parish records.