As Josh61 observes (in a comment above), the saying seems to have emerged in the middle to late 1960s in the context of education. A Google Books search finds seven occurrences between 1966 and and 1968—virtually all in the context of education—and nothing prior to that. I get the impression that the quotation, unearthed from an ancient Chinese source or not, was adopted as a slogan by the "learning through experience" movement in pedagogy.
Here is how the first seven Google Books matches look. From John Williams, Mathematics Reform in the Primary School: A Report of a Meeting of Experts Held in Hamburg during January 1966 (Unesco Institute for Education, 1967) [combined snippets]:
It makes the case for change and refers to such matters as classroom organisation in helpful detail. The title is taken from the Chinese proverb: "I hear, and I forget/I see, and I remember/I do, and I understand."
From Froebel Journal (1967) [combined snippets]:
A group of scientists went to the river yesterday. Where there was a shrimp among the collection in the aquarium, there is today a collage in shades of blue and green, a graph measuring the flow of the river, a section of the river bed, leaf and stem rubbings of water-side plants and a clay image of a shrimp. The separate threads of art, mathematics and science have merged. The resulting yarn is stronger and more lasting — learning through experience.
I hear and I forget, I see and I know, I do and I understand. This was the theme of this year's course. Yes. We heard and forgot, we saw and we knew. And the breath-takingly vital work to be seen in the studio today proves conclusively that we did and understood.
From Official Report of the Semi-annual General Conference of the Church of Jesus Christ of Latter-Day Saints (1968) [combined snippets]:
May I challenge you in the words from the epistle of James to be "doers of the word, and not hearers only" (Jas. 1:22), remembering: I hear and I forget; I see and I remember; I do and I learn. Second Day Others then will follow your example. Teaching will improve. Commandments will be lived. Lives will be blessed.
From Triad: Official Publication of the Ohio Music Education Association (1968) [combined snippets]:
As always, this proverb is an excellent teacher's guide: I hear and I forget/I see and I remember/I do and I understand.
From The Photographic Journal (1968) [combined snippets]:
let me remind you of the Chinese proverb: "I hear and I forget; I see and I remember; I do and I understand."
THE NEWER VISUAL AIDS AND THEIR USES
The overhead projector might be looked upon as the twentieth century version of the old chalkboard. Because it offers a wide scope for invention, while providing a basic service in the classroom, the...
From Independent School Bulletin (1968) [combined snippets}:
Patricia Davidson opened her talk by emphasizing that a Math Lab is not a place but an approach to the teaching of mathematics, and that a school should not feel that the lack of a spare room should prevent its undertaking Math Laboratory work. She quoted Joseph Zimmerman in a statement in which he said that a Math Lab is a state of mind which is questioning and exploring: a state of mind in which the teacher is seen as the catalyst. She also quoted the Chinese proverb which the Nuffield Foundation Mathematics Project has adopted as its motto: "I hear, and I forget; I see, and I remember; I do and I understand."
And from Edward Buffe, Ronald Welch & Donald Paige, Mathematics: Strategies of Teaching (1968) [combined snippets]:
How, when, and why sensory-perceptual materials are used by teachers must be an important consideration in planning for instruction. We would all do well to remember the old Chinese motto: I hear, and I forget; I see, and I remember; I do, and I understand.
At least in the Google Books search results, Confucius doesn't enter the scene until 1972. From John Ingalls & Joseph Arceri, A Trainers Guide to Andragogy (1972) [combined snippets]:
The ancient Chinese philosopher Confucius expressed his belief in the importance of learning from experience when he wrote: "I hear and I forget/I see and I remember/I do and I understand[.]" Confucius related the acquisition of understanding and knowledge directly to living and experiencing. "I do and I understand."
It's not unimaginable that someone preparing for an education conference in the mid-1960s chanced upon a translation of the saying by Xunzi cited in the OP's question and decided to incorporate it in a presentation, at which point other educators latched onto the saying as an expression of ancient wisdom. Alternatively someone might simply have made the saying up (with or without citing it as a Chinese proverb), and it caught on just the same. Either way, once any saying becomes known as a Chinese proverb, it will almost certainly end up being attributed to Confucius before many moons have passed.