3 of his grandparents are Irish
Yes so are mine but that doesn't make me Irish.
Without wanting to open a massive OT can of worms, I think you just have to go with people's own personal perceptions and interpretations. I consider myself Birmingham Irish - born and raised in Brum to Irish parents (who subsequently went back to Ireland). My kids - who are, if you like, the same as Grealish, ie, third generation Irish - still have a real connection with Ireland, support them (and England) when it comes to football/rugby and play gaelic football etc. Basically, the roots can be deep.