RTD sensors and the mystery of Voltage Vs Current sources
Actually, the chip you mention has something close to a current source- because they're measuring the voltage across the reference resistor they don't care if it changes a bit. Since the resistor (connected to the 2V bias) is 4x the 100°C value of the RTD and the RTD only changes by 30-40% for a +/-100°C range, the current is constant within about 10% at a (very high) 4mA for Pt100 and 0.4mA for a Pt1000. That is a much higher current than typically used in precision applications, so self heating is a definite source of error. 

Let's take an example- you want to measure temperature from 0 to 100°C and you have a 0.8mA current source. Let's assume it's a Pt100 DIN curve (\$\alpha = 0.00385\$). 

The voltage across the RTD will be 80mV at 0°C and 110.8mV at 100°C, for a span of 30.8mV. So a 0.1°C error (say that's our allowable error due to the electronics) would represent a 30.8uV voltage, and it would be 0.027% of full scale. 

If you offset the 100 ohm base resistance of the sensor with a stable resistor (it's easy to get a resistor that is much more stable than a voltage or current source), and if we assume that error is relatively negligible, then we still have the 30.8uV error budget, but now we only have to have an accuracy of 0.1% in our measurement (almost 4 times better). A good ADC can be comparable to a precision resistor divider in ratiometric measurements, and that's what the MAX chip is depending on- also they're not shooting for the best possible accuracy, just something viable. 

If you were thinking about using a circuit with, say, a 160mV voltage source and a series 100 ohm resistor to measure the current, you'd have substantially changing current through the sensor (so you'd get less resolution in degrees at high temperatures for a given resolution or noise floor), and the self-heating would greatly increase at low temperatures rather than appearing as a (relatively) fixed offset temperature. A high voltage V with a large series resistance R behaves the same as an imperfect current source of I = V/R with an output impedance equal to that R (Thevenin).