I guess you are right. Sadly, the import of p12/pfx with private key seems to be not possible via the browser. This is also stated in KB18586 if read carefully ...
But at least with 5.0 devices there is another way: I changed the MIME type for p12 on the web server to application/octet-string. The browser can not process the file and asks then if you would like to save it. If you click on "Open" then, the same certificate dialog appears as if the p12 was sent as email attachment
However with 4.5 devices this does not work: If you try to open a p12 on local storage it just says "The returned page had no content type, and therefore cannot be processed". Too bad ... on the one hand, I must change the MIME type to prohibit the processing in the browser; on the other hand, I need the correct MIME type to allow correct processing on local storage ...
Greetings,
Neo3000