In the end, you can specialize in any field from any DO schools.
But attending certain schools help. If the schools been around AND have alumni in the field you're interested, it helps. If the school have a residency in the field you're interested, it helps. If the school is known to have sent students to ACGME residencies, it helps. Look at the rotation schedule for 3rd and 4th year. Are you spending a vast amount of time in required primary care rotation? Do you have electives during your 3rd and 4th year rotations? Do you have inpatient rotations at hospitals where you can make connections?
Not all schools are created alike. Some are betters than others. While it may be popular to state that it doesn't matter which school you attend (and in the end, you can end up in any field you like from any school), certain schools can help you along more than other schools.
Also, cardiothoracic surgery is not a competitive fellowship. In fact, they are hurting for applicants. It's getting the ACGME General Surgery spot that will be the major hurdle for a DO applicant.