I ended up in another county yesterday following a positive LFT with a scratchy throat. The people behind me were from another county again.
Results were back just under 24 hours.
I've only got one tracable contact, and she's now LFTing away. (Although I think the exposure was later that day)
It's not that testing creates cases, but my throat is easily dismissed and once people know they're contacts, the very minor cases get exposed.
When school sends a generic "case in your class" email, there doesn't tend to be a flurry of cases. If a parent declares it on Whatsapp, it seems to go testing mad and a couple of others show up that would have passed under the radar without direct consequence. Then the official local rate goes up.