I can see where you're coming from, here's where I think the landlord would have problems. The "payment minimum" is not clearly defined at all. It could mean anything. The landlord in his earlier post has admitted that he didn't mention the HOA by-laws to his tenants until after they broke the lease. The tenants didn't know this was an issue, again, due to poor communication.
I cna't imagine the lease has any stipulations about when the tenants can use the early termination clause. It sounds like a standard state lease agreement was used based on his previous post.
Regardless, you have to admit this clause is poorly written. The landlord has admitted the lease is absent of any language speaking to an early termination penalty or notice other than this handwritten clause, which was not initialed or dated on this lease. I see it as the tenants went forward with everything acting as they saw the lease termination penalty to be, then upon telling the landlord, had his interpretation sprung upon them. The landlord should've had this clause and his HOA by-law restrictions spelled out much more clearly than they were to his tenants.