The question is closely tied to the existence of "virtual particles", elusive intermediaries in particle collisions whose "paths" appear as wavy lines on Feynman diagrams. The current majority view of them seems to be as expressed e.g. on Strassler's blog, "the Feynman diagram is actually a calculational tool, not a picture of the physical phenomenon", see also Do we need virtual particles? on Physics SE. This was not always the case, in his first diagram paper Feynman clearly reifies "the effect of exchange of one [virtual] quantum between two electrons" (see his drawing reproduced and referenced under What was the first journal to have Feynman Diagrams?). It is a small step from that to interpreting diagrams with two wavy edges connecting two vertices as "virtual pair production in a vacuum" (since outgoing edges representing observable particles are missing).
In fact, they idea predates Feynman. "Virtual oscillations" appeared in the 1924 Bohr-Kramers-Slater paper even before the modern quantum mechanics emerged, and apparently inspired Heisenberg's uncertainty principle. In a 1933 letter to Bohr Dirac predicted the vacuum polarization within his negative sea with holes (positrons) theory, a precursor of QED. As Scholarpedia's article (sponsored by Schweber, a leading expert on QFT history) writes:"In his letter Dirac had succinctly stated the physics entailed by vacuum polarization. The physical picture he sketched... was elaborated by Uehling (1935) and by Weisskopf (1936). In quantum electrodynamics the vacuum is not an empty medium but zero point fluctuations produce virtual electron-positron pairs. These are responsible for making the vacuum a dielectric medium that can be characterized by a dielectric constant, $\epsilon$. This dielectric constant is distance dependent: When a bare charge $e(0)$ is introduced into the vacuum the charge that is observed at a distance R is given by $e(0)/\epsilon(R)$, that is, the observed charge is reduced by an amount $\epsilon(R)$. Uehling determined that the larger R the more screening occurred..." This picture of "dressing up" a bare charge was among key insights leading to the discovery of renormalization.
Then the virtual pair production, this time of photons, reappeared in connection with the Hawking radiation from black holes. Although in his original 1974 paper Hawking does not mention them explicitly, its 1976 follow up Breakdown of Predictability in Gravitational Collapse gives the metaphorical picture reproduced in many popular accounts:"It is shown that the ignorance principle holds for the quantum-mechanical evaporation of black holes: The black hole creates particles in pairs, with one particle always falling into the hole and the other possibly escaping to infinity". The idea remains current today despite the well known ways to derive Hawking's result without using virtual pairs. For example, Parentani's paper titled From Vacuum Fluctuations across an Event Horizon to Long Distance Correlations was published by Physical Review, a leading journal, in 2010.
Let me draw a historical analogy. There is no doubt that early development of electrodynamics was driven by vivid pictures involving ether. Young designed his double slit experiment to mimic waves in a water "ripple tank" he built (see How did Young perform his double slit experiment?), Faraday viewed his "lines of force" as real entities, Maxwell set out to "explain electromagnetic phenomena by means mechanical action transmitted from one body to another by means of a medium", and Hertz believed that he was capturing ether vibrations on his antennas. Then came the Michelson-Morley experiment that failed to produce the expected ether wind. In response, Fitzgerald, Larmor and Lorentz came up with ad hoc contrivances of length contraction and time dilation, which turned ether from almost seen and touched into a forever elusive ghost. The ease with which Einstein dispatched it was largely due to the fact that by his time ether ceased to be the useful heuristic that it was in the 19th century.
A similar dynamic may be at work with virtual particles (and symbolically the not quite empty QED vacuum is the apparent successor to the luminiferous ether), but if the Hawking radiation is their Michelson-Morley experiment then its outcome went the other way. However, unlike in the Rutherford experiments for atoms, or Friedman-Kendall-Taylor's for quarks (see Can quarks be considered real and elementary?) event horizons of black holes do not exactly make for controlled laboratory conditions. Virtual particles are unlikely to be accepted unless more direct and less extravagant ways of "actualizing" them are found, and the jury may be out on that yet.