Manual error in (elisp) Searching Keymaps regarding keymap char properties?

[hokomo]

Hello,

The psuedo-Lisp code presented in the manual (elisp) Searching 
Keymaps says:

(if (get-text-property (point) 'local-map)
   (FIND-IN (get-char-property (point) 'local-map))
 (FIND-IN (current-local-map)))

Why does the condition use `get-text-property', but then the 
consequent uses `get-char-property'? Shouldn't they both be 
`get-char-property'? According to (elisp) Active Keymaps:

"If there is a ‘local-map’ text or overlay property at point, that 
specifies the local keymap to use, in place of the buffer’s 
default local keymap."

Am I missing something?

Additionally, perhaps the two paragraphs in (elisp) Active Keymaps 
that mention the `keymap` and the `local-map' property should be 
reworded slightly to emphasize that the search prefers the overlay 
property over the text property, since that's how 
`get-char-property' is documented to work.

hokomo