A number of variables including differences in string type, thickness, slight changes in the truss rod, neck wood, type and quality of tuner used, etc. etc. all have some effect on intonation, even to a few mm in string length.
I have never seen a bass guitar with all 4 saddles set at exactly the same length, myself.
Cheers
Joe
I’m guessing that when you fret the string, the length from the bridge to the fret wire is longer than from the nut - especially if the action’s high. That might also be influenced by the string width?
I think tension is the biggest factor, that and diameter.
But by tightening a string you change the distance. While an easy touch on a string still leaves some mobility from the point of string contact with the fretboard over the given fret, tight squeeze will remove this mobility, because the pressure and friction between the string and the fret will eliminate all the movement.
Distance remains constant, from nut to saddle. Tension, along with density and diameter is one of the physical factors that affects pitch.
You can test this with two people and a rope, the wave changes with the tension, but the length of rope is constant
consider that strings are not homogenous, they are wrapped and/or have plating applied to them so that changes how they act. Also, the gauge of the wire affects the center line length when you bend them over something.
Make sure your rope is at least 6ft long to maintain proper social distancing 
Absolutely imperative . . . 
You are fine tuning the distance (and adjusting the tension as well) of the standing wave, and in essence moving the exact middle of the wave over the 12th fret.
You can tune a string over a broad (relatively speaking) range of distances on the bass, which moves the midpoint around. Intonation puts it where it belongs.
Each string, being under different tension and having different mass (diameter) behaves differently, thus, the saddles will be in different positions.
Take an 105 gauge E string off and put on a 100.
Pretend we can do this without touching the tuner.
It would be out of tune, so, retune, tension is changed, so that midpoint has also moved a little.
I just set up my fretless and was amazed at how little distance is needed off the line to throw off intonation setup. It only seems like we move the saddle really far, but remember you are retuning after moving it, compensating for tension changes etc.
It’s hard to visualize because you have mass, distance and tension at play.
I’m not sure that’s right - if I have an open string and tighten it, the pitch goes up
You also have density at play; two 100 guage E strings, by different manufacturers, will tune at a different tension and intonation.
considering what “correctly” is, standard fretted guitars have pretty bad intonation 
See the frets at that dreaded G string? 
All analog instruments are compromised in intonation when more than one note is reliant on the same body parts. Some do it well, some don’t.
Saxophones are very bad and rely heavily on the player’s ear and muscle memory in all the tiny muscles in lips and mouth and throat to play in tune correctly. Each note is off a different amount in different directions requiring the player to remember all this without thinking about it, on the fly. . Some mags are better than others at evening this out.
Fretboards are the same, just not as bad.
Aha is that anything to do with temperament? I gather the fret lengths on a guitar do not accurately reflect the music intervals in an octave or something
Its all a balance of compromise, some better than others.
It’s not just the instruments that are imperfect, it’s the 12 tone equal temperament tuning system.
How do you change the tension of the rope without the people moving? The nut and bridge, which the people represent, are fixed in space. So changing the tension would require shortening or lengthening the rope, no?
People would move closer or farther, but the length of the rope is fixed and doesn’t changed. A 10’ rope is a 10’ rope. What changes is the tension.
Physicists use rope to demonstrate waves all the time.
Likewise the distance is fixed on a bass, 34" scale or whatever it is for a particulkar instrument. I know people say by tightening it people say teh length is changed but that’s not the case. The tension is changed, and that’s one of the 4 physical properties that affects wavelength. The nut and the bridge set the length, which is constant.
The four properties are length, diameter, tension, and density. Once a bass is strung, each string has 3 of these 4 properties fixed. The one you can change is tension. You can change diameter and density by changing strings.
But, my question stems from the fact that the “people” can’t move in the bass analogy. So to keep it to the bass analogy, change the tension of the rope without moving the people. If there’s a way to do it without changing the length of the rope (specifically, the rope length from person-to-person), I can’t picture it…