where is the lie though?

It’s a lie of omission.

You’re comparing highly polished mainstream examples of iconic Japanese media to low budget, indie, and amateur american works. If you wanted to be fair the second image should look more like this:

The cultural exchange between American and Japanese art, particularly in animation, is hardly a one way streak.

Here we have Panty and Stocking, which boasts an artistic style that draws heavily upon modern western animation with it’s hard outlines and comical proportions. Shows like Dexter’s Laboratory barrow dynamic posses, dramatic framing, and highly expressive faces form anime and manga. Early anime and manga developed it’s distinct big eyes and childlike features by taking cues from western animation of the 20′s and 30′s

Betty Boop, in particular, was immensely popular in Japan. Her creators even made this short in appreciation of her Japanese fan-base.