A link would be useful to see the context of the quote
One often hears the phrase "most of nuclear physics is in the low energy regime of QCD, where strong coupling constant is large ...",
As it is it is wrong. This is correct
The nuclear force is now understood as a residual effect of the even more powerful strong force, or strong interaction, which is the attractive force that binds particles called quarks together, to form the nucleons themselves
Note the word "residual" which is missing from your quote. It is not enough to talk of low energy regimes of QCD.
Like Van der Waals forces between neutral atoms, the nuclear force is the spill over force coming from strong interactions between colour neutral nucleons.
QCD has three charges , labeled with color indices, and a proton or a neutron are color neutral. There are spill overs from the strong gluon exchanges that bind the nucleons that generate the attraction and known as nuclear force which make protons and neutrons attract each other and build the periodic table of elements. These are of order MeV and distances of fermi, as determined experimentally.
Straight lines are quarks, while multi-colored loops are gluons (the carriers of the fundamental force). Other gluons, which bind together the proton, neutron, and pion "in-flight," are not shown.
In this image we see a possible diagram of the attraction between nucleons, which generates a pion exchange in keeping color neutral at the "large" nucleon distances. The binding between the quarks in the nucleon is much stronger than the nuclear residual attractive force at the energies of MeV. It needs very high energies to drastically intervene in the structure of nucleons, as happens currently at the LHC.
For nuclear energies the plot/calculations have been simplified as a Feynman diagram with a pion exchange.