Any municipal corporation, transit district, rapid transit district, or other public entity which provides rail passenger transportation services through a contract with a railroad corporation, may pay all or part of the share of a grade separation project allocated to such railroad corporation, or all or part of such share of a project’s cost negotiated and agreed upon as the railroad’s share by the railroad and a public agency or agencies pursuant to subdivision (h) of Section 1202.5. In any case where the municipal corporation, transit district, rapid transit district, or other public entity agrees to pay all or part of the railroad’s share, it may enter into the negotiations allocating costs and may be a party to the agreement assessing such costs.