cPanel's AWStats & Statcounter not matching for my wordpress blog

Cool Buddy

Wise Old Owl
I have a blog hosted on Wordpress platform. I have hardly updated the blog for over a year now. Even at its peak some 20 months earlier, it used to get a maximum of 25000 hits per month.
However, I received an email from the hosting company (outpower hosting) a few days back telling me that my site was getting over 2 lakh hits per month and the basic plan was not suitable for it and I needed to upgrade. Statcounter shows around 700 hits per month.
However, AWStats in cPanel shows what they are showing. But look at this:

Now, which site gets less than 0.5% visitors from search engines. Obviously there's something wrong. How do I prove this to the hosting provider? Or are they doing this on purpose to get me to upgrade?

BTW, I want to keep the site up even though I'm not updating it just for the emotional value of it..
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