Look sir, you are bit obsessed with tire sizes, now take a look on these numbers,
Tire size rolling circumference for stock size 145/80 R13 = 1695.55mm
Tire Size rolling circumference for new supposedly recommended size 165/65 R13 = 1642.78mm
Difference = -52.77mm (-3.11%) which means that on speed of 100 Km/h on speed-o meter, you will actually be traveling @ 96.89 Km/h
Let's calculate the same with your chosen size,
Tire Size rolling circumference for chosen size 175/70 R13 = 1734.76mm
Difference from stock size = 39.21mm (2.31%) which means that on speed of 100 Km/h on speed-o meter, you will be traveling @ 102.31 Km/h
For further information, please take a look at following link,
Car Bibles : The Wheel and Tyre Bible Page 1 of 4
Now the normal circumference deviation from stock that is acceptable is +3% / -3%, so your chosen size is pretty much inside the accepted tolerances, you have done nothing wrong, don't seek too many opinions, just enjoy the ride.
Faisal