Very true, but individual income in the US is being discussed.
$15 an hour translates to ~31,200 a year. A household consisting of a married couple or just 2 people living together both earning $15 an hour is $62,400. Pretty close to the median.
Yes, but households by definition don't need to pay two rents, which means if you can afford average rent on $67k, the median household can in fact afford the median rent.
I think you are probably right, median household income likely can afford the median rent. Median rent is ~$1100. After taxes 2 people making $15 an hour are going to bring home $3,900 a month, so after rent that leaves $2,800. Probably a livable amount. To be honest I am not really sure where we were going with this conversation but I agree with all your points :)