It looks like anyone can see the stats for any domain using the service without any authentication. I added the tracking code to my domain and was able to hit https://simpleanalytics.io/[mydomain.co.uk] without signing up or logging in. I was also able to see the stats for your personal site.
Is that intentional? If it is, it seems like an odd choice for a privacy-first service. If not, it seems like quite a worrying oversight in a paid-for product.