With the approval of the board of directors (in most cases), a company can simply create new shares and give them to whomever they like.

I would guess that this information will bother you.

If it helps, because many public company executives are compensated on earnings per share, most C level teams are incentivized to buy back shares, thus decreasing the denominator for the EPS calculation without changing fundamental economics of the company.

If this also bothers you, you should guess what Buffet says and thinks about those two dynamics, and then read up on it, and you will learn something interesting about public markets!

I’m sure if eBay wanted to build 1800 brick and mortar stores they could do so for less than twenty seven billion dollars.

Are they under any obligation to ground the value of their own stock or can a salesman simply claim that the "true" value of that stock is much much more than it currently seems to be?

You understand that the gamestop stock would then be owning ebay, thus be worth Ebay + Gamestops Valuation?