So it seems it boils down to the difference between "delivery" and "processing".
I think we can make this distinction formally. For a given communication channel C, we can define "delivery via C" as a message showing up successfully at the receiver end of C. This definition seems unambiguous.
Now, we can phrase our "theorem" more carefully:
For an arbitrary given communication channel C, exactly-once delivery via C is generally impossible.
The important part here is "For an arbitrary given communication channel C". By adding a layer of deduplication on top of C, we would be constructing a new logical communication channel C', via which exactly-once delivery is indeed possible. But that would be a different channel C', not the original channel C that we were given. In this context, we can refer to delivery via C' as "processing" relative to the original channel C.
I think we can make this distinction formally. For a given communication channel C, we can define "delivery via C" as a message showing up successfully at the receiver end of C. This definition seems unambiguous.
Now, we can phrase our "theorem" more carefully:
The important part here is "For an arbitrary given communication channel C". By adding a layer of deduplication on top of C, we would be constructing a new logical communication channel C', via which exactly-once delivery is indeed possible. But that would be a different channel C', not the original channel C that we were given. In this context, we can refer to delivery via C' as "processing" relative to the original channel C.