We hear this a lot from American politicians. It's a strong indicator that they have no knowledge of the relationship between the Republic of Ireland and the United Kingdom, and have got all their information from drunken songs in Irish bars sung by people who haven't had a link to Ireland (North or South) for generations.
You might like to read more here (and if you can get Biden and the rest of your politicans to as well, that would be good):
The Common Travel Area is a special travel zone between the Republic of Ireland and the UK, Isle of Man and Channel Islands. It dates back to the establishment of the Irish Free State in 1922. This briefing focuses on how the CTA operates between the UK and the Republic of Ireland.
commonslibrary.parliament.uk
I'll point out this quite important statement from it, with the most important bits in bold:
"
Irish nationals have a special status in UK law which is separate to and pre-dates the rights they have as EU citizens.
In short,
the Republic of Ireland is not considered to be a ‘foreign country’ for the purpose of UK laws, and Irish citizens are not considered to be ‘aliens’. Furthermore, Irish citizens are treated as if they have permanent immigration permission to remain in the UK from the date they take up ‘ordinary residence’ here.
This special status affects Irish nationals’ rights across a number of areas, including eligibility for British citizenship, eligibility to vote and stand for election, and eligibility for certain welfare benefits. It is thought that, as a result, Irish nationals have more rights than other EU/ EEA nationals resident in the UK."