This is my first post. I am an amateur pianist. I have been playing for a year, and I have a couple LvB's in my repertoire; however, I felt like giving my two cents on your question. My answer is a definite YES to your question. Should you doubt your piano teacher? Absolutely.
Remember to think about how much time and money you invest into learning the piano? Years, and thousands of $$$. Many practice techniques taught by private piano teachers are discouraged by university specialists. If your instructor is teaching you even one inefficient method for practicing, it can add months (sometimes years) to achieving the brilliant musical pieces you now only dream of playing. I'm not trying to scare you, but through my observations, some have had to completely relearn their repertoire after learning better techniques for playing (the young Franz Liszt took about a year off from concert playing to focus on better technique).
A simple metaphor would be to compare your piano teacher to your primary doctor. If your doctor says, "you only have one year to live," you would more than likely get a reliable second opinion to confirm the illness. Likewise, if your doc says, "see you in a year, you're in perfect health" but you had been feeling under-the-weather, you would likely feel drawn to find a reliable second opinion. You would get the second opinion because your health and well-being are in question. Many doctors make mistakes and mis-diagnoses. Many doctors (although a minority) are simply too lazy to research your chart deeply enough to offer proper treatment, that is a fact. Piano teachers are exactly the same!
Many piano instructors are exceptional, and many are not. A teacher can only teach you what they know.So many teachers teach so many different methods. You can not afford to waste time and money on a teacher who gets defensive when their teaching methods are questioned. A good teacher will welcome students to question their methods, because it is only when these unanswered questions are finally answered that we can move on and become exceptional. If the instructor is kind, and gently explains their reasons for their teaching methods, then they are good teachers, but they still could be wrong. They are human.
In this case, you should not judge the instructor, but the method which the instructor teaches.It's difficult to confront a piano instructor, but a good instructor will not become defensive, but instead will explain why they have chosen certain methods.
A very good instructor will look at their own technique, and figure out why and how they left you feeling vulnerable, so they will not make the same mistake again with another student.
IF a piano instructor gets defensive? You may want to take your money somewhere else! If instructors do not become defensive when confronted, and they proceed to offer a legitimate reason for their questioned instructions, then as i said above, question only the method in which they teach.
I'm not looking for controversy. These are just my two cents. People can accept my advice or leave it. BEST WISHES in your journey!
Jeremy
Edit: I almost forgot to address your question about self-doubt. Is it okay to doubt yourself? I don't think so; however, I will not try to advise you on breaking your problem of self-doubt. I cannot advise you on self-doubt, because I struggle with self doubt myself!! lol

I think it is amazing how the simple process of learning the piano can lead to more deeper lessons in life, or is this just me?
Learning such a complex instrument, and becoming an exceptional player, forces us to look deep within our souls for ability to defeat obstacles in our path. The fact that you are asking the forum for advice shows that you are a pro-active individual, and I BELIEVE you'll get through this. I only have this one advisement.
Focus mostly on being present, in the now, with your music, instead of focusing on the acceptance of others. Enjoy making music.