From an electrical engineering perspective, you’re both right.
ISO in digital sensors is an amplification of the analog signal output by the photovoltaic sensor before it is converted to digital. Amplifiers indiscriminately amplify both noise and your signal of interest. In that sense, he’s right that a high quality sensor with little inherent noise will produce a less noisy image at high ISO than a low quality sensor with a lot of inherent noise. A high ISO (amplification) will serve to amplify noise existing in your signal.
However, amplifiers also have a quality known as “noise figure”, in that all non-ideal amplifiers will add some noise to a signal. So you are also right in that there is some amplifier added noise that is possibly more visible when you increase your ISO, because amplification tends to reduce your maximum theoretical dynamic range through the additive noise, not increase it.
All that being said, this is all semantics and in practice I think the comment you’re replying to is correct, but is a bit loose with some technical concepts that don’t really matter in practice.
There are physical limitations to a phone sensor that you just have to accept at some point. There is some fantastic software that makes the most out of these tiny sensors, but the tradeoff is loss of detail when you zoom in. You can improve your shooting technique, keep a clean lens, add third party lens attachments, but at the end of the day you can't fight physics.
What's your end goal? Are you looking to make prints? Share photos on social media?