Who are the refusers ?

It would follow then that if one loves someone, that one owes them sex, regardless of how one feels about them sexually.
I don't think you believe that.
I love my mother.  I love some of the people I do activities with. I think I love one of my best buddies in a certain way. I love my kids.  
Even in cases where I don't love people, my relationships with them might be intimate. My doctor, my coworkers, for examples.

There are women in my life who DO love me, with whom I have explored romantic relationships with and with whom I enjoy and feel great affection, but who I no longer wish to have romantic relations with, at least in any sustained way. I don't believe you would say I owe sex to them regardless of how I feel? I would say I owe them honesty.

If I love someone like that, does she owe me sex? How's that going to be when I try that line on her? What if I, as you say, offer "my kindness, my compassion, my understanding, my very life"? Does that earn me sex? Do I deserve it - from that person? 

Marriage is no insulation against a change of heart. Relationships and romantic feels swing and shift, sometimes abruptly, for reasons. Whether those reasons are discussed authentically, or perceived cognizantly even -is a different matter- but there are reasons, always. They eventually come out, often in the post-mortem when the fog clears.

My point about empathy for one's partner isn't really about being nice to them or having sympathy for their position, though that might be a byproduct. It's actually a much scarier prospect because empathizing with what you have in common will give you the true scale of what you are dealing with, and will better inform your actions going forward. 

Sex is easy to have if you want to have it with someone who wants it with you.
People have sex all the time, even with people they shouldn't have it with, when the risks and consequences are high, across long distances, or when it's logistically difficult to find time or privacy. They hop in a plane to cross the ocean, they do a conjugal visit to jail, do it in the car, a dark park, in a room with a lock on it, at work - where ever.

So in this kind of situation it isn't that your partner is indifferent about sex, regardless of what she says. It's that she actively doesn't want to have sex with you, for whatever reasons she has. It's not a lack of courtesy or consideration on her part. If she was in a "Why not?" mood, it would be simple enough to say "yes."  Here, on pain of the end of a marriage, lifestyle, family as she knows it, anger from her partner, and hurt, she still says "No". That's not indifference; that's aversion to having sex with you, and it's incredibly painful.

With that in mind, I absolutely 100% agree that it's "about a lot more than just fucking" as you say. It's about what it MEANS to you (and to her, but that's her problem), that she doesn't want to fuck you. As I've found, and many others on here, in the dysfunctional flailing people often TRY to do the fucking as a proxy toward restoring that meaning, but it ends up making it worse. If, as you correctly say, it's not just about the sex, then it's about the desire. So you can have the sex when you know she doesn't desire you - it's going to be awful and you are going to both feel worse. She'll fucking hate you for it and blame you, and you'll learn to hate and distrust your own sexuality too.

What do you have in common with a person in her situation? 

You both are presently choosing to present yourselves as married, in a relationship format that falls critically short of a basic expectation of a marriage. 

You both are in a relationship that is not sexually satisfying, and you are choosing the presentation of marriage and the preservation of other benefits of marriage over the risk of losing them.

You both feel your are compromising beyond all reason, and prioritizing the marriage over sexual satisfaction with others, or at least freedom from the constant reminder of romantic disappointment.

At the moment, for both of you, the price of the status quo is a disagreement and unhappiness at a manageable level with the status quo.

Now, if one of you decides to leave, or an affair is found out, or proposes an open relationship or, or a leave to go to another country for 6 months, something that fundamentally changes the cost, then the whole calculus of the relationship changes, and it compels action. Most people in this situation (me included at the time), try as hard as possible to tiptoe on eggshells so as not to make the cost of remaining in the marriage even higher, fearing its destruction. But the thing that compels action is the opposite of that.  The cost of remaining under the present conditions is unpleasant, but proven manageable by both of you so far. The only thing that compels change is an atom bomb blowing up - not threatened. Then, the choices are either adapt and stay, or get out.

Once you understand that, really understand it and what it means, then you realize that you can't control what the other person does and that they can't control how they feel, then you have no reason to think that the way they feel is going to change. Then it comes down to what YOU are going to with a relationship with a person who doesn't feel the same way about you - stay or leave. That's your agency. If they are staying, then they've made their choice, and she likely feels she's making a noble sacrifice in doing it. What's your choice?