I do not practice in Texas, but in Georgia the proper party to compalin about the association board making repairs on the common areas would belong solely to the owners, not a tenant. If a tenant had been injured, that would be personal to the tenant and they would have a case only as to their injury, but the board is responsible to the member owners.
Contact the owner you're renting from and maybe some of the neighbors who are owners, and get them involved in moving the board to act. Whether it is a potential danger or just an eyesore, if the funds are there, the board has a duty to protect the values in the community as much as possible.
This is not intended to be legal advice or create an attorney-client relationship. If more information is needed, you should consult with an attorney in your state regarding the specifics of your situation and the options available to you.
I agree that the tenant won't have any rights against the HOA. The HOA duties and powers are defined by the deed restrictions, which are a contract between property owners in the subdivision. The tenant isn't a party to that contract, and so has no rights against the HOA. The tenant will have to complain to the homeowner.