Any cheap multimeter will be more accurate than a 3$ battery checker (unless the multimeter is also 3$). I compared different checkers I bought over the years and the only one I found to be very close to a good quality multimeter is this one:
By the way, the cheap checker is correct, as it has only one decimal. It will therefore round all the values up to 4.2V. Even the 4.15 could be a 4.152 which rounds at 4.16 and to 4.2.