Stability of a RF Amplifier
Stability in rf amplifier design:

Unconditional stability - The amplifier is always stable no matter the input and output impedances of the source/load you present to it.
Conditional stability - There's a range of impedances for the source and load for which the amplifier will be stable. If the source or the load impedances are outside this range, the amplifier may become unstable.
If the amplifier is unstable it means oscillations can occur.

I haven't fully read the article and could not find the statement you mention. What I know is that unconditional stability in an amplifier design can be verified using the S-parameters of the amplifier, by checking Rollet's condition:
$$K = \frac{1-|S_{11}|^2-|S_{22}|^2+|\Delta|^2}{2|S_{12}S_{21}|} &gt; 1$$
and that:
$$|\Delta| = |S_{11}S_{22}-S_{12}S_{21}| &lt; 1$$

If you check literature around the formulation of these expressions, you'll also find that if the input/output impedance of the amplifier have a negative real part impedance (not to be confused with the concept you mentioned), then the reflection coefficient at the input/output would be greater than 1, hence leading to possible oscillations.

If positive feedback occurs in an amplifier, means that part of the output signal is adding to the input of the amplifier, this is an essential condition to start oscillation in an amplifier design. As stated before, positive feedback will mean a reflection coefficient higher than 1 at either port, this means the unconditional stability criteria can never be met.