I cannot understand the claim.
As a matter of fact, every quantum symmetry (see below) is the element of a group or, better, the image of the representation of a group. Due to Wigner-Kadison theorem, the symmetry is represented by a unitary or an anti unitary operator $U$. (This fact holds true also in the presence of superselection rules). Next define $G$ as the subgroup generated by $I $, $U$, $U^{-1}$ in the group of isometric surjective linear and antilinear maps in the Hilbert space of the system. $U$ is therefore the image through a (trivial) representation of an element of $G $. Since the group is defined by $U $ itself, there are no problems with phases and multiplicators and the representation is unitary instead of projective.
Clearly, the symmetry is not part of a continuous symmetry group in general. However, if $U $ is unitary, it is always possible, via spectral theory, to write $U= e^{-iA} $ for some self-adjoint operator $A$. Therefore $U=V (t) $ for $t=1$, and where $V (t) $ is the one-parameter group generated by $A $. In this case $G $ can be re-defined as a one-dimensional Lie group (using MGZ theorem to define a Lie group structure) and $\{V(t)\}_{t \in \mathbb R}$ is a strongly continuous representation of that Lie group. Obviously the physical meaning of $A $ is dubious as the construction is quite artificial.
ADDENDUM. Perhaps the problem is with the notion of quantum symmetry.
It is not clear what the authors mean by quantum symmetry.
However, there are in the literature three notions of (quantum) symmetry of a quantum system described in a complex separable Hilbert space.
N.B.: I am referring here to the general notion of quantum symmetry and not of quantum dynamical symmetry (exploited for instance in the statement of the quantum version of Noether theorem).
Wigner symmetry: a surjective map transforming rays of the Hilbert space to rays of the Hilbert space preserving the probability amplitudes.
Kadison symmetry: an automorphism of the lattice of orthogonal projectors of the Hilbert space (representing the elementary YES-NO observables of the quantum system) or, equivalently, a bijecitve convex-linear map from the convex body of (generally mixed) states into itself.
Jordan symmetry: a bijective map from the Jordan non-associative algebra of bounded self-adjoint operators into itself.
In the absence of superselection rules, the three notions coincide and give rise to the same mathematical statement: symmetries are all of unitary or anti unitary operators and the correspondence is one-to-one up to an arbitrary phase.
In the presence of superselection rules described by central projectors of the von Neumann algebra of observables (assuming that the centre of the lattice is atomic) the picture is essentially identical, but the phases may depend on the superselection sector.
In the presence of a gauge group (the algebra of observables in each superselection sector is a non maximal factor), the operators $U$ are defined up to elements of the commutant of the von Neumann algebra, but I am not sure that every symmetry can be described this way and that the three notions of symmetry still coincide.
