ya sayin' that a .500 hose that is squeezed down to a .125 hose.... flows faster
Yep. Absolutely. Velocity is inversely proportional to cross-sectional area.

Water squirts further when you put your finger over part of the end of the hose, and the pressure at the house hasn't changed.

At least that's what I learned in Walter Wan Wang Hu's Fruid Mechanics class when I was a punk young engineer. . .