Well, she's right. Physics is all about problem solving and analysis. I remember one of my physics professors flat out said "If you memorize your way through, you will fail". And I'm not sure how the head of the physics department would be familiar with MCAT scores, but that's good (of course, you can make the case of self-selection etc).
Physics isn't easy major though. Far from it. The math gets messy and you will face yourself struggling with deceptively simple problems for hours. And none of the classes will be an easy A (and surprisingly, not even the calculus-based 101 introductory courses). But hey, as long as you are dedicated, you can do fine.
At the minimum, you need to be strong with math, but more specifically on the side of calculus (single and multivariate), linear algebra and differential equations. Some physics classes may require more (like probability, vector calculus, partial differential equations, complex analysis etc.). It may seem overwhelming, but it really isn't that bad, since you can directly see its applications in physics problems.
Be warned though that you may end up with a lower-than-expected GPA (<3.7). Of course, a strong MCAT can make up for it, but a low GPA still hurts. Coupling that with research and other ECs will be a challenge in the short run, but it can definitely help out in the end, if you do well.
And the key to do well in math and physics is to do a lot of practice problems. Also, feel free to utilize your professor's office hours regularly. It helped me a lot in tackling difficult courses.
