Compact and hard soil are common with alkaline and sodium-rich soils.
I don't dare to try this mixture on my garden, but read the
ingredients on the label and find-out if the EPA or other agencies
have done any research on these ingredients. Many types of soap and
mouthwash contain high levels of Sodium, and other 'strange' chemicals
with peculiar and complicated names. Very likely, even if the person
who told you that didn't make-up the story, It might have a bad effect
on the soil organisms and microorganisms. Do experiments on a plot of
garden with a complete ecosystem (Plants, earthworms, arthropods, soil
bacterias, etc...) and you might need to do the well-known 'before'
and 'after' soil testing.
I use lots of organic matter to mix into the soil. Even if you use
chemicals instead, use the ones initially designated for soil
treatment.