The article says basically "LBYL is bad", but this isn't a good description of what the author does in the later examples. Following "EAFP" without exception is also really bad.
The simple policy is that you should use "LBYL" when you're dealing with local state that can't change out from under you, especially when it's just properties of your local variables, but you need to use "EAFP" for anything that deals with remote state. Function calls can go either way, depending.
Blanket advice against LBYL leads people to use try/except blocks to express basic conditionals. If you want to ask something about your local variables, just ask it in a conditional --- don't make the reader infer "ah, these are the situations which will raise the error, and therefore we'll go into this block if the values are this way". If you want to do something when a key is missing from a dictionary, don't write:
try:
value = table[key]
except KeyError:
return default_value
Just write: if key not in table:
return default_value
value = table[key]
(If you really need to avoid two lookups for efficiency, you would do something like value = table.get(key, MISSING_VALUE) and then check 'if value is missing_value'. But this optimisation will seldom be necessary.)The example the author gives about interacting with the file system is a good example of where indeed you really should use EAFP. The file system is remote state that your function does not own. Similarly if you're doing database operations, calling a remote API...lots of things.
There's various middle ground when you're calling functions. Often you don't want to worry about whether that function is going to be interacting with remote state, and you want to treat it totally as a black box, so you just use EAFP. But if the function documents really clear pre-conditions of your variables you can just go ahead and check, it's better to do that.