Piano is a learned art. There is this huge myth that you have to start early to get anywhere, perfomance wise and musically. Your teacher says the result of what you do is only from hard work, that sounds like a big compliment rather than saying, you have no talent, a talented person could do it much easier with less effort. It is all about hard work, I have never had a student who works hard fail, but i have had students who are incredibly talented but have no commitment, they fail, crash and burn.
Physical playing of piano becomes more and more routine and things become easier and easier. But that takes at least 10 years of focused and guided effort, and full development of your growth, emotionally and physically. The emotional part may take more years, a child working damn hard at 3, will not be a master at 13 if he has no emotional attachment to put his music onto, that comes with life experiences.
If you can maintain that focus and training then anyone can take music as a career, peformance or educational wise. Its just like another job, except a lot of music is done just by yourself, where other jobs you work with other people most of the time. Music, art on a whole is all about self perfection, you will never attain it, but you always get closer to it. It is a mission impossible if you start comparing yourself to others because their progress can blind/dishearten the personal musical journey you take. Focus on what you do, and you will do a lot, there are lots of distractions.