Though the technological capabilities of the timeframe are very ambigious, it is certainly reasonable to suppose that the ability to "send" an entire spaceship and its crew and contents through "hyperspace" would come after the ability to transmit electromagnetic (radio) communications in this manner.
So, if your concern of a plot hole is about the notion that the government seemed to create an extraneous explanation of the ship exploding when it vanished, even though its "secret" purpose was to actually "vanish" by travelling to Proxima Centauri, then that would only be true if the practical aspects of the public story would actually include the ship "vanishing".
Since, in this film's universe, this is ostensibly the first attempt at this "hyperspace" kind of travel, then all that is publicly known about space travel would be about "normal" spatiotemporal traversal across the galaxy. Yes, the spatiotemporal characteristics of electromagnetic traversal in space would mean that for every astronomical unit (AU) of distance away from Earth that the ship was on its journey, it would take an extra 499 seconds per AU for the communications to be received. So, for N [AU] there would be 499N [sec] of "delay" in communications ... if using "normal" space communications.
So, again, if Sam Neill's character had created the technology to send an entire ship and its biological crew through "hyperspace" for traversing the universe, then it is more than reasonable to assume that they already had the technology to send optical and radio communications through "hyperspace" -- a much easier technological achievement, comparably.
This would mean that no matter the distance -- remember the folding paper and the pen scene -- communication would be constant and instantaneous with the ship, the Event Horizon (EH, as you say).
If the Event Horizon would never be out of communication range, then its public role as a deep space probe would be completely bizarre and invite conspiracy theories were it to vanish without a trace -- by entering "hyperspace".
To pacify publication speculation, the story of the ship exploding due to malfunction would completely eliminate its existence, thus justifying any loss of communication.
If this rationale is acceptable, there is then immediately the question of "if they could communicate through the 'hyperspace', why were they not able to communicate with the ship when it was in 'hyperspace'?".
And here is where the plot of the movie enters.
The entire premise of the film -- and why it is one of the best movies ever made -- is that there is no "hyperspace", the technology that Sam Neill ostensibly created is one that actually sent the Event Horizon to Hell.
And it "returned" from Hell, now "possessed" by the Devil, or some demonic presence, which soon infects Sam Neill and other members of the crew.
Sam Neill's character's original technological design was the idea that spacetime could be electromagnetically manipulated through his hyperdrive chamber, such that the ship would ostensibly be projected into an alternate dimensionality of spacetime, wherein the current location and the destination would occupy a nearly singular point in this projection of spacetime, the ship would then travel an infinitesimal amount in this projected spacetime, only to then reproject back into our "natural" Minkowsi spacetime (seemingly: 3-space, 1-time dimension) now at the destination. From the perspective of the ship and its crew, the trip would be instantaneous.
That is why there was the apparent need for the government to create a coverup story. The Event Horizon ship should have instantly "appeared" at Proxima Centauri, but it didn't, they lost all communication -- because it went to Hell when it "reprojected" spacetime. Even though under "normal" communication it would have taken that 4.24 years (or however long), if the technology worked then they should have maintained instantaneous communication through the "hyperspace" provided by the "gravity drive" technology.
Since it truly did vanish, they needed to say it exploded because anyone looking into it would have found out about the "gravity drive", and they didn't want to let out information about a technology that was not only incomplete, but that was inexplicably lost.
I don't think that is a plothole.