Let τ=σ+ν be a point mass perturbation of a classical moment functional σ by a distribution ν with finite support. We find necessary conditions for the polynomials {Q n (x)} ∞ n=0 , orthogonal relative to τ, to be a Bochner–Krall orthogonal polynomial system (BKOPS); that is, {Q n (x)} ∞ n=0 are eigenfunctions of a finite order linear differential operator of spectral type with polynomial coefficients: L N [y](x)=∑ N i=1 ℓ i (x)y (i) (x)=λ n y(x). In particular, when ν is of order 0 as a distribution, we find necessary and sufficient conditions for {Q n (x)} ∞ n=0 to be a BKOPS, which strongly support and clarify Magnus' conjecture which states that any BKOPS must be orthogonal relative to a classical moment functional plus one or two point masses at the end point(s) of the interval of orthogonality. This result explains not only why the Bessel-type orthogonal polynomials (found by Hendriksen) cannot be a BKOPS but also explains the phenomena for infinite-order differential equations (found by J. Koekoek and R. Koekoek), which have the generalized Jacobi polynomials and the generalized Laguerre polynomials as eigenfunctions.