Causative has two meanings: forcing and allowing. Let me first illustrate the semantic distinction considering only "forcing":
- Negation of causative of P = "not force doing P"
- Causative of negation of P = "force to not do P"
In general, there is a mismatch between the hierarchy in the syntactic structure (at the surface) and the hierarchy in the logical structure. For example, the English expression
I cannot do P does not mean "It is possible ('can') for me to not do P" (potential of negation of P) but means "It is not the case that I can do P" (negation of potential of P). What the article is probably saying is that
tabe-sase-nai syntactically looks like the hierarchy is "negation of causative of eat", but its meaning is "causative of negation of eat", or "forcing not to eat".
Now, there is the same semantic distinction for "allowing":
- Negation of causative of P = "not (particularly) allow doing P"
- Causative of negation of P = "allow not doing P"
Note that "forcing" and "allowing" are logically connected under the following
formulae from modal logic (~ = negation, ◇ = possibility operator (i.e., "allowing" in this case), □ = necessity operator (i.e., "forcing" in this case)):
~◇P = □~P
~□P = ◇~P
From this, the expression
tabe-sase-nai which means "forcing not to eat" can also be paraphrased as "not allowing to eat".