Totally disagree with your statement!

Occams razor works well

Expectations are that moving animated objects on or near runways are animals and not human..

when you hear hoof beats in a pasture do you think Zebras??

I agree with you,just have watched some video on utube from a crew cabin at Sheremetyevo takeoff,there is no doubt if the person was going on the runway one would be in sight of crew memb. there was pretty clear weather at the moment over there and i guess either the person was lain on the surface of the rw( there was a restrict visual contact) or crew members were not clear enough with their vision of situation,

"Gatecrasher" perhaps. Trespasser - never heard of it used in that sense. Not that it matters much here, as we can only speculate as to what the crew intended to convey.

If you don't expect to see a person, or animal, on the runway during takeoff, it may take a long time to realize what exactly crossed your path briefly when you have many other things to think about.

Agree.
Only the PF is looking outside, the other one looks at his screen. And the PF looks far away, not under the nose.

Forward look, airspeed, power. Constantly.
With lights you can see several hundred feet. To get hit by an airplane a person would have to be within 10-15 (?) meters of the landing gear when the airplane was a couple hundred of meters away if the plane was doing 130 kts, or more.
The landing lights light up enough to see a person if they're close enough. To hit them at some point they had to be close enough to be illuminated by the landing lights.
Could you do much about a person appearing in your field of view a couple of seconds prior to impact? No. Even if you saw them? No.
And you can't "look under the nose" in an airliner. You can't see anything within 5-10 meters of the nose.
At night you can only see several hundred feet for illuminated objects but runway lights can be seen for miles and miles.
People can look up night time takeoffs on youtube to estimate the forward visibility the landing lights provide. They can look up runway markings to get distance estimates.

I agree there can be some uncertainty. Friend thought they might have hit a deer on takeoff. It came running from his side of the runway. Captain didn't see it and doubted him. Post flight found a bloody deer stuffed in the nose gear well.