That's actually a pretty naive statement. You will get to appreciate the sight of blood, because it actually helps you. It tells you something is perfused. It tells you if you are in the artery or vein when placing a line. It can tell you if you are most likely talking about an upper versus lower GI bleed. And countless other things. Blood is your friend in medicine.
The people who fear blood, pain and fever are the nurses. As a resident, you will constantly be paged that this patient is bleeding through their bandages, or that patient is spiking a fever, or that patient is writing in pain. They will want you to fix these things. However in many cases you may not want to fix them -- you need to see how bad it gets, whether it is self limiting, whether it gets to a level that you need to do something. The last thing you want to do is mask a sign. So you will frequently be keeping an eye on bleeding, on fevers, on pain, without actually giving meds. And this is the great divide between doctors and nurses. Nurses aren't as focused on the big picture, they want to treat the symptoms. A doctor often needs to let the symptoms emerge so he can get the big picture. And as a result, doctors like blood, fever, pain. These are his friends. These are his tools to tell what's what.
So yeah, I disagree that only a psychopath likes the sight of blood. That's like saying a doctor doesn't want to know a patient's vitals. It's a from the hip statement that simply isn't accurate. As I said before, you WILL see blood in med school, in residency. Even after residency, regardless of what field you go into every friend and family member who knows you are a doctor is going to want to show you their wounds/scrapes. If you cannot handle it, or get vasovagal and faint, you can't do this job. The number of times in med school that folks have to change scrubs because they get blood on them is not small. As I said, exposure through shadowing is probably the answer. If you can help doctors stitch up bleeding patients a few times without issues, you will be fine. If not, then I have no clue why you think you can make it down this path.