For the median transaction size of 226 bytes, this results in a fee of 67,800 satoshis
You're misunderstanding a couple of things here:
1. The median transaction size will not necessarily be
your transaction size. The cost of your transaction may change based on the inputs and outputs of your transaction. That's why fees are usually measured in
satoshi/byte.
2. The fee of 67,800 satoshi is for your transaction to be included
in the next block. That site also shows information of how long it may take with a variety of different possible fees.
I found
this to be quite a good article on Bitcoin Core's fee estimation. Personally, I would trust that the estimation is accurate.