I think you might have them backwards? Empathy is the one where you viscerally feel the other person, sympathy is where you can simulate what they're feeling but without that deeper connection, or at least that's how I was taught it.
These are just some of the lies that anyone in a position to make money exploiting people tells themselves, talk to any drug dealer, you'll get similar answers. We all do it to some extent though, the developer creating a heinous subscription cancel flow, the designer making bail bonds ads. You build walls and look the other way. Every one of these actions forces you to give up some of your empathy for the individuals you exploit, the scale at which most execs operate is just mind boggling in comparison.
Also, don't confuse empathy and sympathy - you need to extinguish the latter, but the former is incredibly important to your ability to play suckers.