For any applicant who has executed a document described in subdivision (1)(b) of section 4-111, eligibility for public benefits shall be verified through the Systematic Alien Verification for Entitlements Program operated by the United States Department of Homeland Security or an equivalent program designated by the United States Department of Homeland Security. Until such verification of eligibility is made, such attestation may be presumed to be proof of lawful presence for purposes of sections 4-108 to 4-113 unless such verification is required before providing the public benefit under another provision of state or federal law.