Why is there always such a disconnect between believers in the company and believers who think the stock is underperforming? Are believers in the company really trying to fool themselves publicly and say they (and management) would not want a higher share price?   

What kind of nonsense is this, "And they should not care about the current shareprice at all."?? People, this is a publicly traded stock. One of their simplest mandates is to increase shareholder value. Vis-a-vis, increasing share price = good. 

Higher share price is literally the best case scenario for all parties (except for those not already in).