Again, the point of a data-only attack is that you replace, say, a string with another valid string, and take control of program logic that way. For example, imagine a program that uses `system(LS_CMD_STR)`, where that LS_CMD_STR is some kind of constant holding the value "ls -lah". If an attacker can corrupt program memory in such a way that it overwrites that value with "rm / -f", no amount of assertions will trigger on this, but the program will do something much worse than expected.
In microcontroller programming, redundant data, checksumming and token-passing are sometimes used to mitigate CPU malfunctions due to electromagnetic interference (microcontrollers are often used as "programmable logic", so there's no hard layering between hardware and software, layering violation is made on purpose). If anything looks wrong, you trigger an assertion failure and reset the chip via the watchdog timer. For example, when you pass LS_CMD_STR, you would also pass the name of the caller and the CRC32 checksum of the string as arguments, and the function on the receiving side should validate them.
So I think adding assertion is definitely a way to discover data-only attacks in fuzzing, or even as a partial mitigation of these attacks. It's just stack canary for variables and strings (but as the paper authors said, complete mitigation can be impractical).