If we assume that a general AI can "understand" things in general and can "learn" over time, there is nothing stopping it from understanding the instructions it consists of, and subsequently learning how it can dynamically reprogram itself. If we extend that further, the program could also potentially obfuscate its activity by detecting logging or debugging activity.

That's the way I think about it at least.

All of that is still part of its original instructions.

In a narrow sense, yes. But if the program "learns" self-modification rather than being explicitly told how to do so, and then uses this knowledge to perform operations that were not included in the original instructions, I'd call that a general AI.