Hi, I believe you said it rightly. I found below paragraph form the link you shared, which explains the cause for the question I asked.
A non-redundant protein record that provides organism information at the level of a genus, family, or even super-kingdom does not mean that the protein is found in all RefSeq genomes below that taxonomic classification. It only indicates that the protein is found in more than one genome of different species for which the genus, family, or super-kingdom classification is the lowest common taxonomic node.
Which also means that the taxonomy id which I found locally is more specific compare to online record. Correct me if I am wrong.
Anyway, thanks a lot.
We can assume you're using the same database version locally as the one presented online at NCBI ? ( == your local DBs are up-to-date)?