I agree with the GP on this one that most of those points are not shady. Point #1 is bogus: if you're already doing a venous draw then why do another separate test as well? That's just good sense.
The other points don't especially surprise me either. They seem mostly like either just a cautious response to learning she's a reporter or even standard practice. Many above-board companies who are cautious about their press presence train their employees not to talk to reporters, or to be careful around them, and to report them to the company's PR team.
Reporters don't get everything right, and some have an axe to grind and will twist details to suit their narrative. It's normal for companies to attempt to control their interaction with them.
This strikes me as a cautious response and doesn't even seem especially paranoid to me, or only a little. They have taken really bad press recently and it's not unusual for their employees to have been told by this point to be careful around reporters and to notify headquarters.
Unfortunately the piece does not include a detail that it would have been really useful to know, which is what happens if you walk in and order the one test that can be conducted with a finger prick - would they use their test or not? The difficulty ordering the test that occurred when she asked could have been affected by the fact that she had told him she was a reporter, and the employees freaked out a bit. Those were low level employees who had presumably not been trained on how to interact with the press, but knew about their company's bad situation. I would not recommend reading too much into it.
Plus the reporter almost certainly got Theranos' hackles up by communicating with them and receiving an invitation to have a test done, and then going behind their back to do it anonymously at another center. I won't say that it's unethical for him to have done that, but it's definitely an aggressive action or will seem so to Theranos.