You are missing something basic here, which is that the Sun's corona is rather sparse. To take matters to an even greater extreme, consider the intergalactic medium. The temperature of the extremely sparse intergalactic medium can be in the hundreds of millions of kelvins. However, a macroscopic thermometer in this hot medium would not get anywhere close to those high temperatures. To the contrary, it would cool off, eventually reaching a temperature a tiny bit about 2.7 kelvin.
The temperature of a macroscopic object in space (e.g., a thermometer) has almost nothing to do with the temperature of the extremely thin medium that occupies that space. It instead depends on how much electromagnetic radiation the object is absorbing / emitting, and on thermal conduction amongst parts of the macroscopic object.
Consider the International Space Station. It orbits in a low density medium whose temperature can reach as high as three thousand kelvins. Those high temperatures are not a concern because of the low density. (The drag on the vehicle is a concern.) The Space Station's temperature instead represents a balance between the heat it gains in the form of sunlight versus the heat it loses in the form of thermal radiation into empty space. The heat transfer between the thermosphere and the ISS is numerical noise.
The Sun's corona at an altitude of six million kilometers above the photosphere is orders of magnitude less dense than is the thermosphere through which the ISS orbits. That the temperature of the Sun's atmosphere at that altitude is in the millions of degrees is as irrelevant to Parker Space Probe heating as is the temperature of the thermosphere with respect to ISS heating. What is relevant is that the Parker Space Probe will get much, much closer to the Sun than the roughly one astronomical unit distance between the ISS and the Sun.
The temperature of the Sun's corona has almost nothing to do with how hot the body of the Parker Space Probe will get. The body would cool to a bit above 2.7 kelvins if the probe's sunshield was perfect. It's not perfect; some heat transfer occurs between sunshield and the body of the probe via thermal conductivity. This heat transfer from the very hot sunshield to the probe's body is why the body's temperature will be around 300 kelvins rather than 2.7 kelvins.