Loss on sale of rental property - capital, not 1231?

Below is a copy/paste excerpt from my post on a different thread. I thought a new title would help make the point. It's not that common (in my experience) for a sale of a rental property to result in a loss. But it can happen. And I wonder if many of us would report it as a capital loss.

... made me think more about the interplay among 212, 167, 1221 and 1231.

Sec 167 allows depreciation whether the property is used in a trade or business, or is held for production of income. And we all know that trade or business is a question of fact, in which "regular and continuous" is a factor.

If it's not a trade or business, then unless it's personal, such as a hobby, it's typically 212, production of income.

Property gets special 1231 treatment only if it's used in a trade or business (and meets other criteria).

Sec 1221, in defining capital asset, says

(a) In general
For purposes of this subtitle, the term “capital asset” means property held by the taxpayer (whether or not connected with his trade or business), but does not include—
...
property, used in his trade or business, of a character which is subject to the allowance for depreciation provided in section 167, or real property used in his trade or business;

For purposes of this discussion, let's disregard 1250, 168(k), etc. Is the following correct?

If depreciable property is not used in a trade or business, and is held for production of income, its sale or exchange results in a long or short term capital gain or loss, subject to all the rules that apply to capital gains and losses, and not the rules that apply to 1231 gains or losses, which for losses especially can be an important tax disadvantage.