If the car is going at a set speed, yes, bigger wheel = slower axle speed.
But the car's speed isn't externally controlled, it's a function of the engine and gearbox making the axles turn through lots of revolutions per minute.
Boring maths time->
Using http://www.etyres.co.uk/tyre-size-calculator.htm - 195/65/15 tyres give a diameter of 643mm, multiply by 3.14 (approximation of pi) gives a circumference of 2019mm. So for every rotation of the axle, the car will move 2019mm forward.
70 miles = 112 654 080 millimetres (=112.65km), so it takes 55797 revolutions of the wheel to go 70 miles, if you want to do that in 60 minutes (for 70mph) then that's 930 RPM near as dammit.
So the speedo will be calibrated, more or less, to read at 70mph when it's doing 930RPM at the axle.
Now, let's imagine we whack on some 17" rims, and go to 195/55/17s. These are 646mm diameter, so about 2028mm circumference. So at 930RPM, we go 1886040mm in a minute, or 113 162 400mm in an hour... 113.16km.
Speedo will read the same, as the axles are going at the same number of RPM, but the actual distance travelled in a set time is further - so a higher actual vehicle speed (albeit we're still only dealing with very small percentages, and given that a speedo can be 10% out and still OK...)