I wouldn't spend any more time worrying about this. Even though it is a public record for those who want to spend the time and effort into searching for and finding it, you were not evicted. And if anyone does happen to come across it (which I seriously doubt hardly anyone will) you can just tell them that. This isn't like a criminal record or bad credit that is going to show up in some report. Only someone who has plenty of time on their hands and is super dilligent is even going to come close to finding it. And in any event, you weren't evicted or found liable for anything anyway so there is no judgment against you that is going to show up. There's no need to worry about this.
The property management companies are probably not looking at non-criminal public records; they are looking at the Texas Apartment Association database of tenants against whom eviction actions have been filed. Send a letter of explanation to TAA, and carry a copy of the order of dimissal with you whenever you apply for an apartment lease.