Both inputs have to be at the same logic level,
Where did that come from? Of what use is a gate with external pins forced to a common logic level? The only condition that gives *any* gate usefulness is different logic levels on the inputs.
otherwise any gate could be considered a "universal" gate.
No, any non-inverting gate cannot be a universal gate.
The quote is technically correct, but implies a reasoning path that is incorrect. This is one of the informal fallacies. NOR and NAND gates are universal because they a) have more than one input; and b) at least one input-to-output path is inverting. The implication that both inputs having the same logic level causes a unique output is *not* what gives NOR and NAND gates "universality". The important feature that gives universality is not that there is one unique output for the set of four input combinations, it is that that output is inverted.
While we usually think of combinatorial logic as self-contained and input-directed, it also can be output-directed. An open-collector inverter is the minimal universal gate, but it requires an external collector resistor for combining to happen. Even more minimal is a single n-channel MOSFET (plus an external drain resistor). Along this same line, a ULN200x/280x Darlington transistor driver array makes a *great* universal logic part for high noise and rugged environments.
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