You link to BEST, but BEST is a good example of their strategy. BEST's list of "very rural" weather stations include weather stations in the middle of international airports and cities. Climatologists don't collect their own data, they just scrape stuff from the internet and whatever other random datasets they can OCR so their data is often GIGO.
Obviously if you classify weather stations as rural when they're not, you will conclude UHI isn't important, but this just means you're bad at science, not that the effect doesn't exist. Anyone who has ever driven through a city into the countryside knows that UHI exists and has a significant effect.
https://climateaudit.org/2011/12/20/berkeley-very-rural-data...
The Berkeley classification in Thailand also looks very suspect. As in Peru, many of the “very rural” sites are small cities. Some locations look suspicious. “Bangkok Pilot” is shown as “very rural”, but when googled is associated with Suvarnabhumi, the name of the very urban Bangkok airport (data is sparse, so it may be something else, but anything associated in any way with Bangkok can hardly be “very rural”)
This isn't the only example either. They loooooove to pretend that weather stations sited right next to jet aircraft engines reflect the temperature in the nearest tiny village.