The metaphor of virtual particles that inhabit all of space is used to explain quantum fluctuations. This ceases to be just a metaphor due to the effects of gravity as clumps of any energy (not just matter) in space can give rise to gravitational effects. For example, this is one possible explanation for the cosmological constant.
How can we know that virtual particles exist everywhere in space and not just locally around individual particles or our universe as a whole? Of course, this question may only be meaningful if our universe is actually finite and not infinite (or experiences lonely clumps of matter in vast gulfs of space).
If virtual particles exist locally around the particles that we are using to observe them and not globally then the density of virtual particles would have to rise in value when we put two particles close together to conserve energy. So, I think it might violate conservation of energy if virtual particles did not exist globally. However, maybe there might be tricky ways around this. For example, maybe while the density of virtual particles wouldn't rise the volume of space they occupy would.
Also, a different explanation for the cosmological constant than virtual particles would have to be provided but I do not consider that a real problem because the predicted cosmological constant due to virtual particles disagrees violently with the one observed in reality anyways.
Also, the region of space in which virtual particles occur around a particle would either have to be very big (so that the universe has a great big ball of virtual particles surrounding it and pulling it outwards slightly) or very small (so that there is not a lot of extra gravity pulling things together) [I am not sure this approach would work as I have not calculated how much extra gravity even the very smallest amount of virtual particles would provide].
Maybe it is not possible to prove that virtual particles are a global or local phenomena and we can only rely upon Ockham's razor here.