Now, whether this pressure drop causes underpressure is another matter and depends on whether the effect is stronger than possitive pressures in the system relative to your point of reference (for example, outside atmospheric pressure).
For example, there might be obstruction downstream which means there is already positive pressure in the pipe so the pressure drop from Bernoulli effect is lower than the positive pressure and you still get overpressure (Bernoulli effect is rather weak at slow speeds as it is proportional to square of the velocity of liquid in the pipe).
So, in general, when you have fast flow through a pipe, a hole in the pipe might cause the water to flow out but it could also be sucking air in. It all depends on whether positive pressure is stronger than the effect.
Yes, that is all true. More specifically though, in the particular system we're talking about, gasoline flowing through the main nozzle (which has the same diameter up to the exit) has essentially the same pressure as the ambient pressure. There is an obstruction downstream past the nozzle known as the "splash" which is responsible for bringing the liquid's velocity to zero.
The linked article invoked the Bernoulli effect to compare the pressure of the pumped gasoline in the pipe to the pressure of the ambient air; the Bernoulli effect is based on conservation of energy and does not apply here because the pumped fuel is not magically transforming into ambient air in an energy conserved way.
Now, whether this pressure drop causes underpressure is another matter and depends on whether the effect is stronger than possitive pressures in the system relative to your point of reference (for example, outside atmospheric pressure).
For example, there might be obstruction downstream which means there is already positive pressure in the pipe so the pressure drop from Bernoulli effect is lower than the positive pressure and you still get overpressure (Bernoulli effect is rather weak at slow speeds as it is proportional to square of the velocity of liquid in the pipe).
So, in general, when you have fast flow through a pipe, a hole in the pipe might cause the water to flow out but it could also be sucking air in. It all depends on whether positive pressure is stronger than the effect.