Depending on the size of your chameleon, yes, those are most likely the easiest means to obtain a blood sample. Your vet is not a quack. An intracardiac stick (directly into the heart cavity) is defintely risky, but often the only option in a last resort situation. The vessels of the tail are obviously smaller, but a much safer anatomical site for venipuncture. Unfortunately there is a minimum amount of blood needed to run through common commercial lab testing equipment. A thorough blood panel would be comprised of a complete blood count (which indexes red blood cells and the status of circulating white blood cells) and a serum chemistry (which measures levels of vital electrolytes and minerals[calcium, phosphorus, etc], as well as reflects the function of the kidneys, liver, and other organ systems). A look at what is going on in an animal's bloodstream can yield amazing things!
A large adult cham such as a Panther or Vield can safely handle the extraction of a blood sample large enough to obtain most if not all of the above tests; smaller chameleons by sheer size alone often cannot afford to lose the amount of blood required to run all of the above tests, as their total circulating blood volume in their little bodies is just so small that losing any more than a drop or two can have very unhealthy or irrecoverable consequences. A skillful clinician may still be able to obtain enough of a sample to run even basic tests (calcium-phosphorus ratio, for example) depending on availability of specialized equipment for running "microsamples". However, various circumstances abound that might also affect attempts to obtain a blood sample, namely, the patient: remember that often by the time an animal is presented to a veterinarian in need of a blood panel assay, its more often than not "sick", and dehydration, illness, disease, etc all affect the ease in getting a blood sample. Not to mention a less-than-cooperative, squirmy patient! (To give you an idea of sizes, of the 20or so chams I have right now, only two would I consider large enough to even *try* sampling from, if needed: my Senegal(160g) and my Panther(140g). The Carpets, Jacksons, the wee Leafs...egads! I shudder to even think).
So while a blood sample may offer a plethora of information about your chameleon's health, obtaining that sample is no easy matter at all. If you can find a veterinarian who can run bloodwork on your animals, by all means, bake him/her cookies, wash their car, or whatever it takes to keep in good standing! 
~Kerry
licensed veterinary technician (that's how I know how hard it is to get blood from a chameleon!)