For a marriage licence to be issued three things had to be in the jurisdiction of the granting authority: the residences of the two parties and the location of the marriage. There was a hierarchy of jurisdictions: archdeaconries, dioceses and archdioceses, with the Archdiocese of Canterbury also having powers over the whole of England and Wales. If the parties were from different archdeaconries within the same diocese then a bishop's licence (or consistory court licence) would be needed. If in different dioceses, then an archbishop's licence. Licences could be obtained at higher levels than necessary, and this was particularly the case in and near London as the archbishop's court was located there.
Your hypothesis is that Thomas Axtell of Berkhampstead married Mary Rice of Berkhampstead. The 1638 marriage licence from another archdeaconry implies that neither party to that marriage was living in Berkhampstead. He was certainly living in Bushey, and as her parish is not mentioned, it seems likely she was as well (the original might be clearer). There were Axtell families in Watford and Aldenham, the neighbouring parishes to Bushey, so the simplest explanation for this marriage record is that there was another Axtell family in this area, invisible because the Bushey registers don't survive, of which this Thomas was a member.
If this marriage is to be identified as the hoped for one, then I'd like to see stronger evidence connecting it to the Berkhampstead families. Perhaps the original marriage licence allegation names fathers, gives ages, or has bondsman who are identifiable relatives. Or perhaps there is some other evidence connecting the Berkhampstead families to Bushey. But without something like that I don't see a solid connection.
