Measurements of the off-shell Higgs boson production cross section in gg(→h∗)→ZZ have recently been used by the CMS and ATLAS collaborations to indirectly constrain the total width of the Higgs boson. I point out that the interpretation of these measurements as a Higgs width constraint can be invalidated if additional neutral Higgs boson(s) are present with masses below about 350 GeV.