A bit, but only because your average brit was never anyone's overlord.
Americans won their freedom from the British Crown and aristocracy. The average british person was twice as oppressed as anyone in the colonies which enjoyed much lower taxes and much more freedoms than in Britain itself (despite a democratic disadvantage in the colonies, although I think only the landed aristocracy could vote then, so it was the same for most people). It's not like you could work your way up and aspire to be King, Prime Minister, or city trader; Britain had (and still has) a very strict class system, and well over 99% of the population were condemned to toil in mines, fields, factories or in the street, no matter how hard they worked or how clever they were.
If anything, an educated working class Brit should feel disappointed that the liberation stopped at the coast. It's taken 300 years for the British system to evolve towards a more meritocratic free market democratic system where everyone is created equal, and even now, politics, law, medicine, and finance are pretty much reserved for the middle classes, through cost of entry, and blatant nepotism (the old school tie system - basically the top jobs in these fields are reserved for people who went to Eton (i.e. a few hundred children a year at most), and the next tier is for West Minster School and other second tier establishments, the next tier to those privately educated at less exclusive schools (and with good money), and the rest go on merit). Even today, the 7% of the population who go to private schools (known as public schools in the UK, as opposed to state schools), occupy over 30% of political seats, 60% of journalist posts, 80% of senior banking roles,and 90% of legal roles, which leaves very few opportunities for people who are not in the top 7% of wealth distribution, no matter how hard they work and how qualified they are. Fees for private schools is in the same ball park as the average annual income in the UK.
The other aspect of why the quote is offensive, is that it mocks the relative fortune of Britain compared to the US at a time when the US is at the top of it's influence and economic power, and the UK has had to accept it's status as a small country. It was a hard transition to accept, after being the worlds pre-eminent power and trader for hundreds of years, and people who remember that time probably feel the fall more than those of us who grew up after the 60s.
And finally I would like to wish 'Gung
Hay Fat Choy' to our new Chinese Overlords!