It's not an issue of precision - the issue is that when I play an 800Hz sound the app says it's 121Hz (for example). Unless it's something about my hardware, which seems really unlikely (I've tried multiple mics and instruments). When I use this: https://www.szynalski.com/tone-generator/ to play a 440Hz tone, for example, the app is saying 100Hz. Try it yourself - are you getting a different result?
EDIT: looking at Lobos' DS1 playthrough, the last time I see him retuning the app, all the frequencies he's got buttons assigned to are between 40Hz and 150Hz or so, which is a similar range to what I'm seeing, and doesn't really make sense. 40-150Hz would be a range of less than 2 octaves and he's playing a whole guitar (and those frequencies are way lower than what a guitar plays within). So I think it's a universal problem, he just might not be aware of what frequencies he should be expecting.