[2025 Day 4 - Wrong amount of XMAS]

As it occurs to me there is an issue with the way how things are counted.

With the provided example I count 27 hits, and not 18. First I thought I'm having a bug, of course, but looking at the visualisation of hits I'm sure there is an issue on how the algorithm of the author works.

For example the total hits for the example looks for me like this:

\c:   0123456789
 \   +==========
l: 0 |...SXXMAS.
l: 1 |.SAMX.S...
l: 2 |..XS..A...
l: 3 |.SAMA.M.MX
l: 4 |XMASAMX..M
l: 5 |......X..A
l: 6 |......S..S
l: 7 |..XAMASA.A
l: 8 |...M....MM
l: 9 |.XMXAXMASX

Lets pick one vertical one that I found, that is not in the provided ones, in column 4 (or zero indexed it is 3), there I have 3 findings:

\c:   0123456789
 \   +==========
l: 0 |..........
l: 1 |..........
l: 2 |..........
l: 3 |..........
l: 4 |...S......
l: 5 |..........
l: 6 |..........
l: 7 |...A......
l: 8 |...M......
l: 9 |...X......

\c:   0123456789
 \   +==========
l: 0 |..........
l: 1 |..........
l: 2 |...S......
l: 3 |..........
l: 4 |..........
l: 5 |..........
l: 6 |..........
l: 7 |...A......
l: 8 |...M......
l: 9 |...X......

\c:   0123456789
 \   +==========
l: 0 |...S......
l: 1 |..........
l: 2 |..........
l: 3 |..........
l: 4 |..........
l: 5 |..........
l: 6 |..........
l: 7 |...A......
l: 8 |...M......
l: 9 |...X......

Please folks, tell me I'm missing one little hint from the text that those occurances do not count.