This kind of construction has been called an "internal argument as subject" construction, but is more broadly known as a "middle construction," as in between active and passive. It strikes me as not particularly unusual, if maybe a little bit literary.
For example, from Massam (1991), where "_" marks the empty structural object:
This article analyses middle constructions in English, accounting for their
key syntactic and semantic properties. The analysis rests on the observation
that there are certain similarities between middle, tough and recipe-context
null-object constructions, such as in (ia-c).
(i) (a) This bread cuts _ easily.
(b) This bread is easy to cut _.
(c) Take bread. Cut _ carefully (and arrange _ nicely).
Here are some more examples of IASCs, from the same article:
(7) (a) The brown bread cuts easily.
(b) This blouse washes like a dream.
(c) The soup that eats like a meal. (Campbell's advertisement)
From the author's conclusion, which I will attempt to summarize at the end:
In this way, middles
are claimed to ... involve non-thematic chains which are licensed by being co-indexed with a chain which does receive a theta-role [and to] involve empty reflexives which do not arise via Move-α
but which are base-generated. ... The view of middles utilized here is one which considers their defining
property to consist of an element of modality which appears in INFL and
which is usually further spelled out by an overt adverbial or modal element.
It is this element which is able (universally) to license a non-thematic subject
which serves to identify a null object.
In other words, the author of the paper suggests not that "paper" moves from the object position to the subject, but rather the presence of an adverbial like "well" or "easily" (or a modal*) allows for the use of a patient** as a structural subject in an English middle construction.
After all, it would be odd to say "?Paper cuts" to mean "Paper is cuttable."
So in other words, the fact that you want to say something like "You can cut paper easily" allows you to instead say the English sentence "Paper cuts easily," which is indeed ambiguous with "Paper cuts [other things] easily."
That some people analyzed your title as one or the other depends on the fact that paper is both cut often and cuts people frequently (after all, we have the word "paper cut"), and it just depends on which association came to mind more easily for each person.
For example, me, and other people who interpreted your sentence as "paper is easy to cut" might have been thinking about scissors gliding through paper.
* An example of a modal licensing middle construction is "This blouse won't wash" (p. 126, example 27.f).
** In linguistics, the patient is the recipient of the action of the verb, as in "Mary cuts the paper."
Massam, D. (1992). Null objects and non-thematic subjects. Journal of Linguistics, 28(01), 115. https://doi.org/10.1017/S0022226700015012