OIS.
As you mention over and over that Cornish miners were very skilled at what they do.
Based on their expertise handed down generations it seems they would have known digging a vertical shaft without wall support would be highly dangerous AND IMPROBABLE.
If they didn't know this, then they were not as experienced and skilled as you suggest.
The first thing a skilled miner would do is take a sample of the dirt. Using his knowledge of previous shafts, i suggest they would say...
"hmmm, clayish till, not a good sign. This isn't the stiff clay like we have in Cornwall so we probably need to use wall support to be safe."
Or as you suggest, they would say...
"hmmm, clayish till. Well, we know how to use cribbing when digging vertical shafts but thats only when the crew are a bunch of cowards. However, this crew is really, really brave, so damn the cribbing! We're NOT going to use any support to prevent cave ins until we get to 100ft mark where we start digging horizontal tunnels.. then we'll use cribbing!"