Based on what? You're basically saying, "the air isn't holding a solemn stillness because it isn't."
I think "The air holds a solemn stillness." is perfectly equivalent to "There is a solemn stillness in the air."
Keep in mind I'm not arguing just articulating my personal interpretation
If we break down the original sentence we have:
"...a solemn stillness holds,"
To me the subject verb relationship is quite clear hear. The only difference is that in modern English we'd have the object last, but in this case it comes first. It remains (in my mind) that the object is 'all the air', again emphasizing that the stillness exists before the air.
I think if the verse was trying to say that a stillness "holds" where holds = remains, exists, stays, etc., and that the air is the subject that possesses the stillness as a quality or function of itself, we'd need some kind of preposition or something. For example:
"And
in all the air a solemn stillness holds."
But I do not think the 'in' is meant to be there (obviously it's not there but I mean, it's not there in meaning or unspoken sentiment either), so the arrangement of the stillness pre-existing the air seems like the poetic meaning here.