Yes, that's exactly it. The system that copies DNA is itself encoded in DNA. The DNA produces the tRNA, that copies the DNA. There is no DNA coding for producing tRNA that attaches to a stop codon and any mutation that produced such a tRNA would almost certainly render the containing organism non-viable.
Also. Some vertebrate codons act as invertebrate stop codons.
I believe you are over-generalising here. While some groups of single-celled organisms & organelles do use a slightly different coding system to that used in most prokaryotes and (IIRC) all eukaryotes, it is not the case that veterbrate and invertebrate codings are different.