Unfair advantage means:
1. Interview questions for fresh grads are very CS oriented. For example, I have seen candidates immediately dismissed for not being able to estimate algorithm complexity. Same for memory requirements. Same for variants of knapsack problem. Same for not being able to get to alternative approaches. Good luck getting those questions right without spending 4 years doing CS.
2. Internship. CS grads get 2-3 very solid internships on their resume. This comes up during the evaluation as a big factor.
3. The "he is not a CS major" comment popping up during the reviews unintentionally.
4. Cultural fit (very true for other industries as well). People hire people like themselves. CS grads have a lot more in common with other CS grads.
Google/Facebook/Microsoft/Amazon/Apple/LinkedIn/etc are at the top of the food chain. If you want to be the best, you have to compete with the best.