I know a lot of patients, including the ones here, research their T online. That means the T has the right to do so. And, your T revealed that they were doing so, which is very honest. The T did not have to put it on paper but behaved ethically and did so.
In summary, if the patent can research about he T online, the T has the same right. And, she put it in writing. you did not have to accept it.
Also, did you ask why your T wants this information? There might be a rational explanation for it.