No, they do not have standing to evict. They have standing to bring a breach of contract case against the OP but NOT standing to evict.
You keep saying that and you are still wrong. They DO have standing. The Illinois Condo Act SPECIFICALLY provides for that remedy (as previously posted).
(a) In the event of any default by any unit owner, his tenant, invitee or guest in the performance of his obligations under this Act or under the declaration, bylaws, or the rules and regulations of the board of managers, the board of managers or its agents shall have such rights and remedies as provided in the Act or condominium instruments including the right to maintain an eviction action against such defaulting unit owner or his tenant for the benefit of all the other unit owners in the manner prescribed by Article IX of the Code of Civil Procedur
The suit is PROPER. The PROPER people have been named and the association has standing.