This is 100% correct. But nothing stops Sony from expanding Bungie's studio in the near future, with the intent to make a PS exclusive. For example, what if Bungie wanted to create a VR Warplane Dog shooter? By default that'll be exclusive to Playstation, unless they create it for Vive and Oculus too. But that wouldn't come to Xbox for obvious reasons.
There's no reason to believe Bungie within the next 3-5 years wouldn't be creating a non-Xbox game to be honest.
As happens with all their other internal studios, they are also highly growing Bungie or at least announced plans to do it in the following years.
Bungie games will be on rival consoles like Xbox. But these multiplatform games could get exclusive betas or demos on PS, console bundles, short timed exclusivities of some DLC (like 1 month) as we saw in places like CoD, could be exclusive regarding game subscriptions. Or maybe even the games themselves could have a very small timed exclusivity but as of now they seem to be planned as full multiplatform.
Seems Sony is doing the same MS did for Minecraft or announced for big Bethesda or Activision IPs. There may be some console exclusive but I think most of these exceptions are going to be timed console exclusives and that will focus on multiplatform instead.
But yes, if Bungie makes some VR stuff obviously is going to be console exclusive (I don't think they would be capable of including it into Nintendo's cardboard VR).
Obviously plans can change, and over time Bungie (or Sony) may decide to keep Bungie exclusive. But as of now their plan is to release their Bungie stuff everywhere. Sony and MS want to grow by releasing on more platforms including rival consoles.
I think Sony will buy another -pretty likely Japanese- multiplatform publisher and to keep it multiplatform. But to keep them exclusive for betas or demos, game subs services, VR stuff, console bundles and maybe to get 1 month timed exclusivity or something like that for some DLCs.
I think MS will do the same on their side with Zenimax and Activision Blizzard. They get exclusive betas/demos/bundles/game subs/timed exclusivity for some DLCs but the games get multiplatform with maybe some exception from time to time (like a new IP, some niche game or a game from a small team).
They bought these companies because they make a lot of money and have been very expensive, it would be dumb to turn them into full exclusive specially now with the chips shortage. They make more money by keeping them multi.