ECG can cause safety issues if there is a significant current across the sensor leads, but even that is unlikely unless the completely wrong resister values used and the person hypothetically has a heart condition.
Disclaimer: I'm not a physician, neurosurgeon or lawyer. I did however design and repair EEG systems.
Most hobbyist designs, like the one in this article, do not have such protection. Indeed, for this particular circuit, a simple static discharge, as might happen when you're applying the electrodes after walking over carpet, can fry the input amplifier, connecting it to the power rails. ESD (and, indeed, defibrillation -- which is about a thousand times more energy than ESD) protection would be present and required in any medical biopotential amplifier, even unrelated to the single-point protection described above.
If the ESD failure happens to short out to power rails, your current will be your power rails divided by your electrode impedance. This distribution is described in EC11/EC13 (although electrode technology has improved since the days when those tests were done, so impedance is even lower). Even with the ancient electrodes in EC11/EC13, you would get unsafe currents some of the time. With modern electrodes, you would get unsafe currents much of the time.
I've seen dozens of circuits for home EEG/ECG/EMG. Almost all of them, including this one, are a deathtrap. They will work okay most of the time. At some point, someone's going to kill themselves.
Disclaimer: I am not a physician, but I've designed ECG circuits all the way through safe, successful human trials.
Most of the "danger" comes from poor isolation. The skin resistance is too high for EEG to cause major problems. I realize the actual standards have requirements that are detailed and somewhat strict.
The difference is that ECG has sensors that can directly put current through the path to the heart so the risk is higher if there is a worse-case ESD latchup. 5mA is enough to stop a heart in certain conditions.
EEG isn't ECG or EMG and have different characteristics even though they seem vaguely similar.
PS. My contact info is in my profile.
With electrodes, the current can be /much/ greater than touching metal wires with a finger. Single-digit kilo ohms is typical. The big ECG paddles are tens of ohms, probably.
Another way to think about it -- have you ever felt even a 24v battery? No. Now You know that 9v tingling on your tongue? That's saliva and a tiny contact area. Now think of a large patch of engineered electrolyte can do.
That alone is a massive problem - how do you know? Most people only discover things like this when things start going wrong. And if you make things go wrong, then you risk doing even more damage. I've never had any of the tests done professionally, but I imagine there is a certain amount of assessment that takes place before the tests are even conducted.