There is no denying the fact that strong acids can possess negative values of pH due to the following reasons:
1. The strong acids do not dissociate completely at high concentrations. Some hydrogen remains bound to the chlorine so that actual H+ concentration is less and the observed pH becomes more than what is expected from the molar concentration of the acids. 
2. As there are so few water molecules per formula unit of the acid, the influence of H+ in the solution is enhanced. In a way, the effective concentration of H+ (or the activity) is much higher than the actual concentration. 
3. The usual definition of pH as -log [H+] should be better written as pH = - log [aH+] (negative logarithm of the hydrogen ion activity). This effect is very strong and makes the pH much lower than what is expected from the molarity of the acid. 
4. If we dip a glass pH electrode into the 10 M HCl solution and measure the pH, we observe that pH is higher than the true pH. This is awell-known defect in glass pH electrode measurements and is called the "acid error". It is sensitive to experimental conditions and difficult to correct for.
Lastly, the pH scale of 0 to14 has been arrived at simply due to the reason that the kW, i.e., {[H3O+] [OH-]} of water at 25C is 10^-14; meaning thereby that the concentration of H3O+1 may vary from 1M or 10^0 to 10-14M.