I don’t think that first part is completely correct . Bacteria that stumble into the blood stream are often destroyed immediately via the complement system and then somewhat unexpectedly by red blood cells . The chance a white blood cell would randomly bump into a free floating bacterium is fairly low. If you have a large number of bacteria in your blood stream your immune system has failed significantly in containment and can be life threatening as there is no way for the host to mount a vigorous immune response within the vascular system itself and within seconds the bacteria can find their way to distant targets normally impossible for them to reach. I guess I only see the people where this system has failed so maybe I’m biased , but we see bacteremic patients all the time. Often immunocompromised and/or with poorly controlled diabetes. They may have septic emboli into the lungs , liver brain, spleen, spine , and for some reason the psoas muscle is a popular landing spot. But the blood steam is almost alway quickly cleansed of bacteria once antibiotics are started even tho primary infection is still active. Blood is a hostile environment