I sent my parents a prepaid US SIM-card in the meantime.
The reason, why I think the kiss and fly might be the better choice for me, is that I do not have to expose myself to the terminal-curbside-craziness on a Friday afternoon.
Understood. Those of us familiar with T5 will say that if you spend a couple bucks to park it is really very easy to navigate. Arriving pax go up a level from arrivals and then there is a overhead walkway that takes you right to the parking area, no craziness, you don't even cross traffic until you hit the lot. The only trick is to watch for the signs to International short-term parking as this is very separate from the other parking areas. The lot is sort at the closest edge of ORD, so you never hit any of the main access areas, just a quick entrance/exit into the T5 lot.