It's the same logic as refusing delivery of a shipped good when it comes to contract law (IANAL). It's expected that when a good arrives, the buyer pays. If the buyer refuses to pay then the good is not 'delivered.' In the transition to services the 'delivery' is the invoice you get and that is the moment you are compelled as the buyer to pay that invoice. If you start paying it then you have accepted the invoice as valid because you paid for part of that invoice. Given this the context of being sued would be that the seller observed that the invoice was valid by the buyer paying something towards that invoice, and therefore they should be compelled to pay the rest of the invoice.

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.