10 Reasons Why The New Doctor May Actually Be River Song
4. The TARDIS And The Sonic Screwdriver
Another explanation as to why Martin's Doctor may be River Song in hiding is the TARDIS. As within the Doctor's timeline, River and the Doctor are married and it can be presumed that upon the death of the Doctor, the TARDIS will become River's. Perhaps the future death of the Doctor the TARDIS to a young River Song - perhaps even to Melody Pond.
This would explain how Martin's Doctor can so comfortably fly the TARDIS, even if she is River Song. In fact, we have witnessed River fly the TARDIS before, even correcting the Doctor about the handbrake! This may also explain the basic design of the TARDIS's interior. It has been handed to a new "owner" and thus it, too, regenerated into a blank canvas to be personalised by River's regenerations.
There is also something to say about Martin's Doctor being too "smart" for the sonic screwdriver, while each Doctor from William Hartnell to Jodie Whittaker has had one. Perhaps, Martin's Doctor is not the Doctor post-screwdriver, but rather River before. She has not yet met the Twelfth Doctor within her timeline, and it is Capaldi's Doctor who gives her the screwdriver.
Their timelines are backwards from one another, what was the Doctor's becomes River's.
It is all wibbly-wobbly-timey-wimey.