>The scenario you introduce is different from the specific line I was responding to. My intention was to show that some more consideration and rework of the idea could bring more clarity.
In your example you are choosing to accept interruption of service in exchange for a preferential rate.
Net neutrality preserves the integrity of internet access by stating that ISPs may not interfere with traffic based on it's origin or destination for competitive reasons (e.g. to coerce payments from service providers a consumer may choose to access). The core premise of Internet access is that a consumer is paying for access to the Internet. If a consumer chooses to permit the service provider to modulate service at the consumer side in order to gain preferential treatment (better price, etc), then this is a consumer choice.
> I could have a switch to change my water heater to the non-interruptible service if I needed to use it during a time of peak demand. How does "pay more for priority" fit into the net neutrality picture?
There are numerous ways to "pay for priority"; even with electricity you can pay a supplier to upgrade capacity in your area to ensure that you have the ability to more consistently draw power, especially at peak times (granted this is not a trivial process). With Internet access the same thing is available - if I want a 10Mbps connection, that has minimum bandwidth of 1Mbps at peak times, and 99% uptime, then I could reasonably expect to pay more than someone who only wants a 1Mbps connection, can tolerate a minimum bandwidth of 512Kbps at peak, and only needs 90% uptime.
This is not a net neutrality issue, and this should be consumer choice (I am old and from Canada, so the numbers above are low :P); allowing lower cost terms of service for less guarantees is a time honored tradition in delivering utilities and services, but most utilities in many parts of the world have a minimum standard that must be met to achieve regulatory compliance for consumer services (e.g. water pressure upper and lower limits, natural gas line pressure, electricity amperage and voltage, etc). Anything above that regulation-blessed "consumer grade" is an opportunity to extract value for priority, and is compatible with net neutrality.
The Net Neutrality issue is that your provider can then regulate the service which you have bought and paid for (network access to your ISPs network peers, and via those access to the Internet) to prevent you from access resources from specific sites and resources, and deliberately applying QoS to degrade a users experience with those third party sites and services in order to coerce the upstream services to pay the ISP.
This is why I say that a service that does this is not Internet Service, but rather a curated network service.