Rewatching the new episode, there's definitely something interesting in the subtle ways the Doctor undermines Belinda throughout the episode, as well as the fact she immediately clocks onto it, having dealt with the same bullshit in other relationships (Alan and her housemates) and her job.
The most obvious is when the Doctor scans her DNA without asking and she immediately pulls him up on it. There's also the fact he:
Glosses over her concern about him knowing where she lives and following her everywhere.
Kinda glosses over her being the one who puts the plan of combining the certificates into action, while considering it a success due to Timelord biology alone.
Boxes her into this "mystery girl" narrative, which resonated perfectly with Ruby and many others, but Belinda is not impressed by in the slightest.
Continues to call her "Miss Belinda Chandra" on the TARDIS, even after she's made it clear she doesn't like being called by her full name.
And these aren't complaints about the episode in the slightest, because there is this underlying assumption that the Doctor, as much as they love humans, will always be smarter and more sophisticated than human companions could ever be.
I can definitely see the comparisons to Rory, because, as he said, the Doctor does put people in more danger a lot of the time! People put themselves in that danger to impress the Doctor! And considering Belinda has no way home if the Doctor does decide to take her on a whirlwind adventure regardless of her wishes, that's a pretty terrifying position to be in. Especially after almost being coerced into marrying her extremely controlling ex-boyfriend.
Overall, looking forward to seeing how this goes. If nothing else, maybe the Doctor will learn something new from all of this!