Just because something looks like a "viral" infection caused by a virus organism infecting cells does, not mean the viral protein has come from outside the human genome or from a separate genome.
The human genome has many dormant and polymorphic genes that can create new "viral proteins" that can be programmed by the human DNA to do all types of functions.
For instance messenger RNA can be coded specifically by the DNA and acts very similar to how you have presented the virus organism acts.
Naturally made mRNA will be carried in nanosized packages of exosomes which can express specific proteins to latch onto cells and force the production of new proteins that the messenger RNA has told the cell to make.
This looks identical to how you suggested a virus organism spreads from cell to cell growing and releasing copies of rna or dna copies of itself.
Also just because a cell absorbs genetic proteins does not mean the cell is being hijacked.
Through endocytosis and MHC domains the cell will break down these proteins or antigens and then the cell could be programmed to differentiate into an antigen presenting cell that recognizes the parts of the antigen or genetic proteins that it absorbed and broke down.
This can create all sorts of enzyme sequences and one can be for messenger RNA to send this code to other cells to make more antigen presenting cells. Another enzyme can be made to make viral proteins such as antibodies like cytokines and interferons to destroy damaged cells or help clean up and regenerate cells.
Might I add these viral proteins are mediated by exosomes also.
Interferons are added to these exosomes packets to control the cytokines and if the cell is deficient or DNA is damaged these exosomes can be mispackaged and cause uncontrolled cytokine destruction or other defective disease loops.
Most of these so-called virus organisms are simply proteins made by dormant genes from the human genome to get rid of a toxic load of antigens and free radicals; the viral proteins are not making copies of themselves to destroy the cell as a separate virus genome. This theory might seem exciting or interesting but there is no evidence to this.
If these virus organisms were real and operated the way you say then we would have no chance of survival.