This! I've parked at all the London airports except City numerous times all without serious issues, and I'm fairly crap at parking (see below). Some multi-storey ramps can be stressful because the Model X is so huge, and my missus who is a much better parker than me also experiences this. It's surmountable though. We've definitely clipped a few curbs with the wheel trims, but never any bodywork scrapes. That said, I've driven a few performance models with low-profile tyres, and if you drive over anything bigger than a grain of sand you'll chip those wheel trims. Stressful!
The worst parking experience I've had was in a multi-storey car park in Cardiff, when I managed to parked exactly alongside another car. If you'd've asked The Stig to park more closely, it couldn't be done. We're talking physical contact at both the front and back wheel arches, but not enough to scratch or damage anything: literally less than a millimeter, you couldn't see light through it; you couldn't have gotten a sheet of paper between us; there was hardly any space to turn the wheels. I had one of my staff in the car because we were returning from a work trip, and I had to spend forty-five minutes slowly teasing the car back out, much to the amusement of passers-by. We had to resort to stuff like raising the suspension to try and gain a few microns of clearance. My employee turned this into company folklore of "the time I went extreme parking with Deejay."
The lesson here: don't as as talentless as me at parking 
