Is it true that an isolated fundamental/elementary particle does not decay?
It seems logical to me.
No, because not all the fundamental particles (in the sense of the standard model) are stable. In particular, electrons and photons are stable; muons and tau leptons are not, and will decay into lighter leptons, e.g. $\mu^-\to e^- \bar\nu_e \nu_\mu$.
Neutrinos are kind of funny because, while they are prevented from decaying in the traditional sense by conservation of energy, momentum, and lepton family number, they do oscillate - so if you start with an electron neutrino, for example, it will turn into something that can be observed as any flavor of neutrino, and in this way you can find yourself measuring something like $\nu_e\to\nu_\tau$. But then you can just as well measure $\nu_\tau\to\nu_e$, and if you have two (actually three) particles which can all decay into each other, does it even make sense to call it a decay?
Quarks try to be funny but actually wind up just being annoying, because they are never found in isolation so nobody is exactly sure how an isolated quark would behave if you could put one in a universe by itself. That being said, heavy quarks (charm, bottom, theoretically top) are routinely observed to decay in high-energy collisions, where asymptotic freedom presumably applies, so it's not much of a stretch to imagine that an isolated heavy quark would decay into lighter quarks plus a pion or leptons.
Likewise, the weak gauge bosons decay all the time in collisions, so if you managed to create a universe that contained only a $W^\pm$ or $Z^0$ and nothing else, it would presumably decay quickly into a lepton and antineutrino or into some combination of hadrons. Same goes for the Higgs, except with different possible decay products.
It's only true if you take "isolated" to mean "isolated for an infinitely long time", in which case, an unstable particle would never form either. An isolated particle is exactly stable, this is the S-matrix state, and the exactly stable particles in our world are the electron/positron, the neutrino, the photon, the graviton and some dark matter.