Is Heisenberg uncertainty principle really a demerit of Bohr model?
The text is actually describing the observer effect, which is very commonly confused with the Heisenberg uncertainty principle. The latter is a far more fundamental property of the Universe, and has strong theoretical backing (the non-commutativity of certain mathematical operators in quantum mechanics), regardless of experimental setups. The uncertainty relations thus establish a fundamental "fuzz" to any object, precluding its complete and precise characterization even in principle. 

The lack of the uncertainty principle is indeed a severe conceptual limitation to the Bohr model (or rather it is better to say that the lack of the groundwork which results in the Heisenberg uncertainty principle is a limitation); whereas the Bohr model still makes predictions in terms of the classical concept of orbits, a more fully-fledged theory of quantum mechanics applied to an atom necessarily predicts the formation of orbitals, where the position and momentum of the electrons is smeared out.

Indeed, the uncertainty principle is ultimately why electrons have stable configurations around atomic nuclei that stay on average around 100 picometers away from the nucleus. The nucleus itself is only around 1-2 femtometers (~0.001 picometers) in diameter, so electrons could have their potential energy greatly reduced if they closely hugged the nucleus at a similar distance. So what's stopping them? If the electrons did scrunch up so tightly against the nucleus, they would essentially be localizing themselves in space very accurately, and thus the fundamental uncertainty in their positions would be very small. However, because of the Heisenberg uncertainty principle, this would cause a very large increase in the uncertainty of the momentum, which in turns causes a very large increase of the average momentum and from there a large increase in their kinetic energy, so that the electrons would ultimately need a higher total energy to stay so close to the nucleus. Again, this behaviour is completely independent of whether the system is being measured or not.

Furthermore, Bohr's model is actually very empirical. In particular, one of its most important considerations is that the angular momentum of the electrons around an atom obey the formula $m_evr=n\hbar$, where $n$ is the positive integer responsible for introducing quantization to his model. However, this is just a postulated equation, with no rigorous derivation. It was chosen because it happened to describe the emission spectrum of hydrogen exceedingly well, so he knew it was right in at least some regime, but had no proof for it.