Wait really? How so? It's not like they would otherwise lack sufficient evidence to show you showed up and received care, right? I would've thought acknowledging would just restart the clock, which would've made no difference here.
On the other hand if an invoice is never realized because it's in dispute, then you have a stronger leg to stand on. A different way to look at is in sit-down dining. You receive service, you are delivered a bill, you are then expected at the moment the bill is delivered to review it and pay it, and if you pay it the bill is settled. If you have a dispute because nobody ordered a diet coke, then the bill is rejected and hopefully sorted out before a final bill is presented and people pay for it. The same sort of logic ends up applying here. If you paid for half the meal and left that has different outcomes compared to not paying the bill and causing a stink.