Exercise 12.3.3 - Untidy solution?

[JNNielsen]

https://jrnold.github.io/r4ds-exercise-solutions/tidy-data.html#exercise-12.3.3

I believe there is a problem with the solution of this exercise, because the solution generates untidy data.
Please correct me, if I am wrong.

In the solution for this exercise, the "people" tibble

people <- tribble( 
  ~name, ~key, ~value, 
  #-----------------|--------|------
  "Phillip Woods",  "age", 45,
  "Phillip Woods", "height", 186,
  "Phillip Woods", "age", 50,
  "Jessica Cordero", "age", 37,
  "Jessica Cordero", "height", 156
)

is widened like this:

pivot_wider(people, names_from="name", values_from = "value")
#> Warning: Values are not uniquely identified; output will contain list-cols.
#> * Use `values_fn = list` to suppress this warning.
#> * Use `values_fn = length` to identify where the duplicates arise
#> * Use `values_fn = {summary_fun}` to summarise duplicates
#> # A tibble: 2 x 3
#>   key    `Phillip Woods` `Jessica Cordero`
#>   <chr>  <list>          <list>           
#> 1 age    <dbl [2]>       <dbl [1]>        
#> 2 height <dbl [1]>       <dbl [1]>

However, as I understand it, the resulting tibble is untidy, since the column names e.g. "Phillip Woods" are themselves variables.

Instead, I think the authors intended the pivoting to be done with names_from="key" and values_from="value", resulting in this tibble:

# A tibble: 2 x 3
  name            age       height   
  <chr>           <list>    <list>   
1 Phillip Woods   <dbl [2]> <dbl [1]>
2 Jessica Cordero <dbl [1]> <dbl [1]>

In the r4ds book https://r4ds.had.co.nz/tidy-data.html the column names also seem to be updated to reflect this, as they are now called "names" and "values" instead of "key" and "value":

people <- tribble(
  ~name,             ~names,  ~values,
  #-----------------|--------|------
  "Phillip Woods",   "age",       45,
  "Phillip Woods",   "height",   186,
  "Phillip Woods",   "age",       50,
  "Jessica Cordero", "age",       37,
  "Jessica Cordero", "height",   156
)