Companies issue shares. These shares are listed as a liability on the company's balance sheet. Each share represents a liability to the company because it entitle its holder to a share of any dividends paid by the company.

The intrinsic value of a share is the net present value of this future stream of dividend payments, not its current market price. OP's point is that the market price of a share can be significantly above its intrinsic value in periods of irrational exuberance, such as now, creating "paper wealth" that doesn't really exist and which will evaporate when the speculators head for the exit.