Ah - yes, I can see how that would be annoying.
Maybe two points:
1.) There are a multitude of ways to get things into Devonthink, and honestly would recommend that – assuming you want to make a serious go of it – you spend a bit of time on the Forums/with the manual, learning about the various options.
Depending on what approach you use, the file will either be dropped into the so-called Global Inbox (which is at the very apex, and requires you to manually feed it into a specific DB), or you can be prompted in what group you want the file, or you can drop it on specific folders/drop-points on your system, that then have folder-actions running, and feeding those files to specific groups.
Of course, the beauty of it all, is that you can run a variety of these, or all of them, which will cover just about any variation to getting files in.
Off the top of my head, I use the following:
a.) Clip from Safari, using the toolbar droplet/shortcut key – asked where I want to place the file;
b.) Using the Devonthink ‘Sorter’ window, either dropping the file into a particular Inbox of a DB, or a particular folder/group of a particular DB;
c.) Mail rules inside Mail.app to Devonthink - sends mail that matches the necessary criteria to DTPO;
d.) Drag and drop into DTPO or onto the Dock item (my dock is hidden, so I seldom do this, but have at times);
e.) Using the Finder Sidebar Inbox location, most frequently in conjunction with Default Folder X; and
f.) Numerous Finder folders (including Dropbox etc.) that are either being Indexed, or have a Folder Action associated with it, to import the files.
I think the above covers all of them, but there might be more glaringly obvious examples I am missing!
2.) On your point about how DTPO doesn’t like your changing of files, when opened externally – that would suggest you were importing your files into the DTPO database. To be clear, it is really simple to get things out, but one must be mindful of the fact that if a file is imported, then – as a general rule – any changes to that file’s name etc, should happen inside DTPO.
You can change it externally, but since DTPO isn’t ‘watching’ to see what you do to that PDF when you open it in an external reader, if you go and make filename-data changes to it, that make the change on the actual file sitting inside the DTPO db, then that file can become ‘orphaned’, since DTPO hasn’t been aware of the changes you make, and so cannot update its index to know what that file is now named.
Note, the fixing of an orphaned file is relatively straightforward, but the best practice is simply not to change filenames etc., unless you do it inside DTPO. That said, you obviously can annotate/re-order/change/delete pages inside the file, using an external application, as long as the filename isn’t being effected.
The ‘fix’ to the above, which is probably what would most interest you, is to simply INDEX files, rather than Importing them.
Files that are Indexed by DTPO, do not ‘reside’ inside a DTPO db. They remain where they are, inside your Finder structure. DTPO is basically watching the Folder (so one must be a bit circumspect about not moving/changing the Folder itself - but this can be cured by having DTPO index the topmost/apex folder, leaving you to move things freely below that uppermost folder), and as long as this Folder can be ‘seen’, you are free to make any changes you wish to any files/sub-folders below that.
[Ok. Maybe that’s a bit of an oversimplification - but the main point stands. 
One needs to experiment a bit in the beginning, to be sure one understands how DTPO and Indexed files operate – but it’s a fun way to learn things, and doesn’t take long to grasp, if you do rather than read !]
So you can delete/rename/copy/annotate/merge/add/consolidate etc. etc. to your heart’s content, as you would normally do, inside Finder – but having DTPO watching those files/folders, gives you all the power of DTPO in terms of search functionality, and its AI, along with - subject to some caveats - moving/splitting/dicing up the data inside DTPO.
I think its fair to say that most users probably have a combination between Imported and Indexed data inside DTPO, as opposed to only Indexing. Many (I would presume), probably started out there DBs with a complete Import, and then added more Indexed folders to the mix.
But the point of the above, is that the differences between an Imported library, and an Indexed library, whilst subtle, is significant, and might explain why you were running into the stickiness of trying to manipulate Imported files, as if they were Indexed.
This reply was far lengthier than anticipated. Apologies. But maybe something in the above will help!