I suppose we could use Taq Pol on canid DNA because DNA is DNA, whether in a bacterium or in a dog. Chemical compounds work similarly in similar environments. This is just basic chemistry.
Mish already pointed this out to you, Taq pol works on that canid DNA because of evolution, specifically because of common ancestry.
Even by your standards, that could only vaguely be true. You know that the phylogenetic tree is subject to revision at any time, as it has been several times even in the last few years. You know that new discoveries frequently change the depiction of evolution at all but the most abstract levels. It is only in this generalized form that evolutionary theory even has any application in medicine.
Says the guy who seems to take pride in not understanding evolutionary biology? This is incorrect, evolution has many applications and implications for medicine. Whether you are talking about the use of antibiotics, antivirals and anticancer chemotheraputics and designing new drugs, to understanding disease incidence and susceptibility in populations (do you plan to never work with sickle cell patients in your endeavors in medicine?).
Oh maybe you want to be a heart surgeon then so all that evolution mumbo-jumbo wont matter? Be sure not to clip the recurrent laryngeal nerve as it takes an absurd rout off the vegus, under the aortic arch and ascends back up neck to the larynx. Or maybe you ought to understand the nature of hernias how the spermatic cord passes through the abdominal wall collecting bits of apaneuroses along the way. Or why so many people have back pain. Or maybe why congenital diaphragmatic hernias happen? Or any of the other numerous bits of our anatomy that are explained by our evolutionary lineage.
Oh, sure, for some definition of the word, evolution is occurring and can be observed.
This is creationist talk, not science talk. Biological evolution has a specific definition--In science we are about specificity. The biological fact of evolution is that allele frequencies change for a population across generations.
Theory in science, we use to explain facts. In this case we use theory, like natural selection, genetic drift etc, to explain how those allele frequencies change across time.
Insisting the evolution is some "vague" term that describes the big bang to man as one mechanistic process is what the dishonest creationists want you to believe and what the gullible and ignorant creationist actually believe---Because of their refusal to learn what science actually says.
"Relatedness" is in terms of best human judgement, not any purely objective measure. That's why a board has to review how the tree is arranged; the phylogenetic tree is a judgement call.
Phylogenetic trees can be both a model--as a type of scientific theory used to make predictions based upon evidence or they can objective representations of gather facts--Such as those based on gene mutation rates. It depends on what the tree is being used for. Of course that is something someone who actually studied evolution should know......