Coins are briefly visible as they are mined so you can count them manually as they enter supply. You can also run a Monero node and have it audit circulating supply for you. No different from how every Bitcoiner verifies in practice
I just see Bitcoin as another tool as well. It does some things better than Monero and some things worse. And to be honest Bitcoin and Monero are both just mediums of exchange at the moment. Neither really meets all the criteria for a money.