What puzzles me is…how does she [DiDonato] has control on her voice if she, in your opinion, sings with looseness of air? I mean, her voice would collapse because of the lack of air, or sound strained, and it doesn’t sound strained, nor she has any external sign to support the sound with the throat.

Actually, many singers sing with loose air and don’t sound strained. It might be more correct to say they sing with a lack of compression. Compression of the breath is not only a matter of using the breathing musculature. It is also a matter of the proper resistance of the larynx. When the larynx “leans” into the breath it creates stability and puts the breath into a compressed state. That is what’s lacking. She sings very well, but in a completely different manner than I am trying to describe.
Also, I do not understand when you say her voice is too fat. It sounds very well-aligned and I refer to her live perfomances not to her recordings. She’s got a slender medium voice, solid high notes and good low notes for a lyric mezzo.

When I say it is too fat I mean it is enlarged by breath rather than being completely tone. It doesn’t have to be breathy in order for there to be breath in the tone. It is hard to notice if you haven’t experienced it and learned to hear the difference.
Maybe, I fail to notice things well, I don’t know, because I can’t say in what point her voice is not clear. I don’t hear any breathiness or muffle area in her voice.

Don’t you think is possible to sing with control of the pressure and, at the same time, use the flow to release tension without sounding breathy? Because it seems to me she does exactly that. One actually sings on the air (sul fiato), but also with the air. I believe it’s one of those paradoxes of singing.
No, I have to say I don’t think that is possible. If there is balance there will be no tension. So there is no need to release a flow of breath to release the tension. Tension exists because of the release of breath. If the larynx is properly opposing the breath pressure in a coordinated way the body will have no need to create tension in the throat. Throat tension appears when the body is trying to compensate for a lack coordinated action. The biggest cause of this is uncoordinated breath that is escaping through the phonation. The body senses this and creates tension in the throat to compensate for the lack of stability.
The meaning of the concept to sing on the air means the larynx on the breath. Not the breath flowing out and the tone is on top of it somehow. That is fantasy of imagination not physical reality. If you sing with the air that means you are letting air out as air and not as only vibration. You can’t do both, they are mutually exclusive. The air that does escape is what is naturally part of the vibration as rapid puffs. But not a constant flow of breath. 
I pointed her because to me she seems to have a perfect emission, or at least, the less compromised one amongst contemporary singers. But I’ve never seen her live, so I can’t say any further.

I agree that she is less compromised than many other examples we could use. (i.e. Fleming) She has developed skill in the ability to hold the pharynx open to hide the breath in her tone. A singer functioning naturally doesn’t have to hold the throat open, at least in the same way. The stable larynx and proper pronunciation pretty much take care of it and the throat stays open almost by itself. This is what I mean when I say the open throat is a result of complete function, not a cause of it.
This endeavor of illustrating the natural function is kind of difficult because we don’t have examples of this type of singing that we can hear live on a regular basis. If we did it would be much easier to recognize it. But the big difference is in the immediacy of the tone because of its purity. I have talked to people who heard Jussi Bjorling live describe how they would hear his voice a little sooner than the other singers in an ensemble. It wasn’t because he was ahead of the other singers musically, he was right on the beat. It was because of how his voice was functioning. It had no wasted breath in the tone. This kind of pure tone travels better acoustically. So it not only starts more spontaneously, but it reaches the listener faster as well.
These same people also pointed out that his voice was not really “big”. But they could always hear him the best, even at the back of the theater. This is really what should be considered quality over quantity. Loud or big singing doesn’t carry. Pure singing may seem loud and big in a sense because it is intense. But the singer can’t try to sing loud or big or the results will be a disaster.
Don’t worry about some comments, for reasonable people know your analysis are not to belittle the artistry of these people.

Thank you. And thanks for contributing.