It protects you for that debt.
However, the company may be saying you paid that one, but there is another one they are dunning you for.
You need to hold onto those proofs for dear life, and if those are on some sort of online service, you need to print them out, several copies, and capture a PDF. Online services are notorious for shutting off your access to documents after a time period. One example is the US Postal Service will only show "proof of delivery" of mail online for 90 days. After that, they figure you have resolved your eBay issue or whatever. However, the IRS moves much slower than that, so you can get a rude surprise when preparing for tax court.
The bigger problem is your credit report
The company does have the option of putting a black mark on your credit report. You may not care now, but it will stick for seven years. It will affect your ability to get credit, rent a home, and get a job.
One legal option is a legal action to silence the question. You use this when you have dangling uncertainties: you fear another person might sue you, or they are considering avoiding court and taking lesser actions such as collector harassment or a credit report burn.
So you can force them into court, saying "There is a dispute between us. They say X, and I say Y. I am asking the court to resolve this now." Exhibit A is the proof that they did sell you a product or service at a price, and Exhibit B is proof you did pay for it.
Really, it's their job (not yours) to prove they sold you something, but here's the thing. If you do a good job showing their side of the argument, it makes you look fair and reasonable to the judge... and if they don't have anything to deny or add, they may not even show up. That's not an automatic forfeit, the judge will simply decide based on the facts you've presented.
This sounds like an open-and-shut case, and the size makes it just the kind of case small claims court is for.
Once the court rules you do not owe the debt, they cannot engage in collection actions, and credit reporting agencies must remove the mark.