You were lucky that you ran into the ideal case at every step (quality of people, trustworthiness, company performance, etc.), except for the initial invoice hiccup. Your experience is the very rare exception.
After being in your position repeatedly I learned that most cases are not this. Clients would just refuse to pay with reasoning that was sometimes legally solid even if clearly malicious. I ended up having to go to court again and again to get the invoices paid, which meant getting paid years late and with a haircut from unrecoverable court fees. Sometimes it wasn't even worth it to go to court just for a pyrrhic victory, or there was nothing left to go after.
I'm scratching my head now to remember a single case where the inability to pay was due to genuine impossibility followed by good will, rather than "because we can". They'd go to extreme lengths to not pay their debts, all the way to bankruptcy and usually reappearing a day later with a new name and a clean sheet.