Many recombinant proteins have optimized codons that give great expression in Cos or HEK cells, and others including baculovirus and other non-mammalian cellular systems such as yeast and insect cells. Certain mammalian proteins do not express well or at all as native sequences in non-native cellular systems, but can be optimized with regard to codon usage. I have substantial experience at this, as this is commonly used as a work around strategy for gene patents in the past.
Vinmantoo mentioned in his original post though that he had known some examples of altered protein activity with the apparent same protein sequence. I am eager to read up on such examples.
What threw me was the use of the phrase "protein activity". Your first example is correct but not accurate due to semantics. The activity of each single protein has not been altered by the mutation, but rather levels of the protein in the cell are reduced resulting in physiologic or metabolic changes. The second example is not correct as removing an entire exon will change the primary sequence of the protein.