There is a lot of confusion about PDOC. Part of the problem is that the usual way we find out that the PDOC is there is that the MOBI turns up in the Docs app (vs the Books app) on the Fire.
I may be adding to the confusion, but what I now think is true is the following:
a) There is a metadata field in MOBIs called cdetype (number 501). If this is set to EBOK the ebook will show up in Books, otherwise (no cdetype or set to PDOC) it will be in Docs.
b) Calibre does not add cdetype to its own MOBIs (e.g. created by converting from ePub). It adds cdetype when writing a copy of the MOBI via "save to disk" or "send to device".
c) In Preferences -> Output options -> MOBI output. There is a "Personal doc tag" option. This is typically set to [PDOC], but it can have any value you want. The way this works is that if
this tag is associated with your ebook in Calibre and
you are writing a copy then
cdetype is set to PDOC and otherwise
it is set to EBOK.
Note that, based on my tests, if the "Personal doc tag" option is set to [EBOK], the cdetype is still set to PDOC if you have added [EBOK] as a tag to the ebook in Calibre. So changing it from [PDOC] to [EBOK] would only have an effect if you have [PDOC] as a tag to your ebook.
One thing I am not sure about is how Calibre knows that the MOBI is Kindle-bound. Some of the reported issues on the Fire makes me wonder if there are additional undocumented requirements. Note that in most cases we don't know that Calibre-generated ebooks contain PDOC - we just know they don't contain EBOK. Also, I'm not sure what happens if the existing MOBI in your Calibre library already contains cdetype set to PDOC.
Anyway, based on the above you should not need to reconvert your MOBIs (except perhaps if they already have a cdetype of PDOC).
If you are familiar with the command line, MobiPerl
's mobi2mobi command will printout all the metadata in a MOBI. There is a precompiled version for Windows, so you don't need to install Pearl to use it. Using this command on the same ebook in Calibre's internal folders and on the Fire might be informative.
EDIT: The Java Mobi Metadata Editor
can be used to check (and edit) cdetype, and make be easier to use than mobi2mobi.