An authority shall constitute a “hospital corporation” as that term is used in Division 2 of Article 4 of this chapter; and any county otherwise authorized to do so may designate any authority having the power to own and operate health care facilities situated in such county as the agency of such county to acquire, construct, equip, operate and maintain public hospital facilities in such county, in the manner and with the consequences specified in said Division 2. Such authority shall, if so designated, receive the proceeds from any special public hospital tax referred to in said Division 2. Further, the reincorporation hereunder of any public hospital corporation that has theretofore been designated as the agency of a county to acquire, construct, equip, operate and maintain public hospital facilities in such county shall in no way impair or invalidate such designation, and such reincorporated public hospital corporation shall continue as such (with the consequences specified in said Division 2) just as if it had not been reincorporated hereunder. Nothing in this section shall, however, be construed in any manner to limit any rights or powers otherwise conferred upon an authority pursuant to any other provision of this article.