Wikipedia states:

The classifying space (geometric realization of the nerve) of a symmetric monoidal category is an infinite loop space.

If my mind is correct, Segals delooping machine gives a functor $Sp$ from topological symmetric monoidal categories $C$ to prespectra (In this question, a presepectrum is a sequence of based spaces $X_0,X_1$,... with structure maps $\Sigma X_i\rightarrow X_{i+1}$) with $Sp(C)_0=BC$ the classifying space of the category.

If I remember correctly, one of Segals results is that the adjoints of the structure maps $Sp(C)_i\rightarrow \Omega Sp(C)_{i+1}$ are weak homotopy equivalences for $i\ge1$ and for $i=1$ this is the case iff $\pi_0(Sp(C)_0)=\pi_0(BC)$ is an abelian group with the induced multiplication which comes from the fact that $BC$ is a commutative monoid up to homotopy.

So the classifying space of a topological symmetric monoidal category $C$ can in this sense infinitely delooped only if $\pi_0(BC)$ is a group.

I ask myself:

1.) Did I say anything stupid or wrong?

2.) Is Wikipedia wrong?