Is natural language more fine-grained than CIL ?

The following example was proposed:  (A) 'Mary knows that she likes herself' and  (B) 'Mary knows that she likes Mary'. 

(A) corresponds to    $comb_{(0)} link_{\{\{1,2\}\}} comb_{(\star, 1)} K link_{\{\{1,2\}\}} L \,M$

(B) corresponds to     $comb_{(0)} link_{\{\{1,2\}\}}  comb_{(\star,1)} K  comb_{(\star,0)}  LM \,M$.

We note also that $\lambda$CIL can be given a another form.  Instead of using $comb$ we use application and for instance $\lambda x. D^{(2)}x T$ (assuming $\eta$-equivalence).