Not true at all. There is a constitutional mechanism, amendment, to change a constitution that is no longer working, or desirable.
Let me give you an example of the perils of a "living" constitution, the commerce clause: "[The Congress shall have Power] To regulate Commerce with foreign Nations, and among the several States, and with the Indian tribes". "Among the several states" has been reinterpreted to mean "within every state". This "living constitution" has led to an encroachment of federal power to now, quite literally regulate anything the federal government wants. The reinterpretation of the commerce clause is the legal heart of the war on drugs. The misinterpretation of the commerce clause is the basis of the Raich decision. You can rightly lay the blame for the drug war at the feet of the "living constitution" disciples.
Roe V Wade is another example of an extra-constitutional reading of the law. Personally, I happen to like the right to choose an abortion (within limits, see the other thread), but that does not change the fact that the Roe decision is insupportable from a legal perspective.