>my understanding is that there are various sets of data files: one set describe all the “raw sets of temperature measurements” the BE team could find
Where did you find that phrase about measurements? On the data page
>Source data consists of the raw temperature reports that form the foundation of our averaging system.
a report may not need to be based on a measurement and on the about data set
page it is written:
>Best value series: "Best value" time series were formed by averaging across multiple records when they existed at the same site. In addition, flagged values were dropped and previously manipulated GHCN-M and Hadley Centre data was ignored in favor of other data sources when possible. These series are expected to be the primary records for most future studies, but the fully-flagged and multi-valued records will also be preserved and made available for more detailed analyses.
In short I found no explicit statement that real measurements (and no description how these were performed) were used and as said for the gridded data they mention that they use a
>reconstructed monthly temperature anomaly