Tony,
To the extent of my knowledge of the PSE you're correct. That is to say I really only know how to use the PSE insofar as it enables one to interact with NX assemblies. I gather there may be a bit more to it than that, but then there are plenty of things you can do using Teamcenter that go over my head, even after a few years of exposure to it. We prefer to change the content of the assembly ONLY within NX, and not by editing it via the PSE. We only use the PSE to un/lock it precise or to load latest released or latest working, and to create baselines. The good news seems to be that if you alter its structure by using the PSE and don't subsequently open and then save the assembly in NX, then you can always just open NX and then open the Assembly which will give you the original structure and virtually discard your PSE changes. If you prefer that, as opposed to accepting changes that purchasing might like to foist upon you, then it's good news, otherwise you're in danger of losing work.
The system I'm used to has an item master with a dataset item, the NX part file, and a product structure item, under that also, but only if the part is an assembly. Ownership is conferred to only one user at a time via the item master. Meaning that who owns the item master owns everything under it. There are generally a couple of other items under the master sometimes a JT file for VisView, and often a drawing manifestation or an altrep for installed parts. This is true of the GM and Opel systems as well so I've never seen it set up any differently than that. I don't want state with any certainty that it cannot be otherwise, but I had naturally assumed that was just the way it worked.
So to answer your question, if the ownership in your implementation is conferred via the item master then others having the ability to change things probably means that either there is no ownership given to the files, or that everyone is using the one login, (or both). If you have separate logins then you can deal with the ownership crisis in at least two ways that I know of. One is to workflow the files and assign them to your user, who should then possess ownership until they are released. The other is to check out the files manually so that they stay checked out. That will force others to ask before they can save their changes to your item masters.
I won't go any further mainly because I only know just enough to keep myself out of trouble in teamcenter that is properly used and if anything over managed. Should you not know what I'm vaguely talking about I suggest you really get some help with it, and I say so because if you are using it in an out of control way then I fear that you'll wind up in a great big mess that will be very difficult to overcome indeed.
Good Luck with it
Hudson