There are two types of people who don't shampoo every day: those who don't wash their hair every day, and those who wash their hair with water most days but shampoo only some days.
If your girlfriend is in group 2, then your experience is relevant to the parent's post; if she is in group 1, then you haven't yet experienced the difference.
I'm in both group 1 and 2 (I normally alternate between the two, i.e. soap - water - soap - no wash - soap...).
Washing with soap removes oils. This is a pretty obvious effect from anyone who's ever tried to clean up oil/grease with soap (ex: dawn).
Rinsing with just hot water distributes oils from the scalp down towards the ends and it removes a little bit of oil in the process.
Rinsing with cooler water is less effective at distributing oils but also loses less oil in the process.
Not washing allows grease/oils (and skin/dander) to build up on the scalp and saturate hair near the scalp.
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If you are just rinsing/scrubbing with water, it does a lot relative to not washing at all but there isn't really a comparison when it comes to soap's efficacy at stripping oils/making them semi-water soluble so they can be washed away.
There are two types of people who don't shampoo every day: those who don't wash their hair every day, and those who wash their hair with water most days but shampoo only some days.
If your girlfriend is in group 2, then your experience is relevant to the parent's post; if she is in group 1, then you haven't yet experienced the difference.