I see a lot of people equating the presence of thought with the mind itself.

Examples?

it follows that a "Silent mind" is one where there are no thoughts running around

No, it could also be that people equate the presence of thought as one manifestation of mind and not entirely equating it. Furthermore, silence/stillness can manifest in the form of unobstructed and steady awareness of non-still or non-silent phenomena.

I believe the silence that is being referred to in a "silent mind" lives in the space between each thought

This is common, most famously advocated by Eckhart Tolle (most famous in the US), [saying things like](http://www.awakin.org/read/view.php?tid=519 'Pay attention to the gap -- the gap between two thoughts, the brief, silent space between...'

While this is true in some sense for finding literally silent displays, but if we're talking about the mind being silent, then you can also have silence that encompasses the words and their intermittent spaces.

Meditation is losing the attachment to "My mind"

meditation is tons of things to tons of traditions. if someone said, 'REAL sports are X,' you would reply that 'sports' is a label that applies to many activities that aren't X.

Meditation, some would argue, is about losing attachment to the mind and everything — full stop. Whatever appears, even a sense that the appearance is 'in a single mind,' is just an appearance — 'an appearance in what?' Well, whatever it is it's already there or behind all things you could point to.

Who is the one returning to the breath

Yes, and whatever appears to be that which returns to the breath is also an appearance. In what? I don't take that metaphysical leap, not necessary. Furthermore, 'who is returning to the breath' often just makes people move their awareness away from the appearance —the breath, the whatever— and into another appearance that they think is that which returned to the appearance. It can be done right, but I have rarely seen people do it without a good Vedanta style teacher.

Breath awareness can be a great tool to help one learn how to be aware of the present moment. But I think there needs to be a point in everyone's practice where the practitioner is brought into question along the lines of, "Who is the one returning to the breath?"

Well, I rest in the nature of mind which happens to occasionally do breath-awareness practice —in order to steadily reside in the nature of mind. Some people have a tough time understanding that transcendent practices encompass everything, including eating, exercise, studying, and that includes moments of mind-cultivation.

I think that as your practice advances, it will become less and less of your practice and more and more of a simple residing as pure awareness and presence

If one must make metaphysical statements, I guess you could say that it's possible to view some parts of practice as objects 'of pure awareness and presence' while still doing them.

you who think that the mind can only be clear when thoughts are silent

I don't think people believe this for the most part, mindfulness practitioners are vocal about not needing to stamp out thoughts in order to feel peace. But some people who are starting out with meditation are so deeply tumbling that I wouldn't tell them to bypass stabilizing meditation because it's merely 'literal' silence of the mind. In order to even witness the things you're saying, people need to experience a true breaking of mental spells. Some people need to first see a clear chuck of dead silence to be confident that peace of mind is possible, and I don't fault them for needing to see that to believe in some practices.

look at the silence that is always present regardless of whether a thought is allowed to be

that which looks at the ever-present silence that popping up between the thoughts is also intrinsically silent. the sense of inner silence is a sense held subtly by a transparent process that I wouldn't want to describe too much but others have called silent and truly all-encompassing.