SVM behavior when regularization parameter equals 0
First, the remark from the wikipedia article deals with small (positive) values of $\lambda$, not $\lambda=0$.  Indeed, if $\lambda=0$, then every separating hyperplane achieves the minimum score of 0.

If the data is linearly separable, then taking $\lambda$ small enough that the first term dominates ensures that minimizing the loss will require taking a separating hyperplane to zero out the first term, and subject to that minimizing the second term is equivalent to the original hard SVM.