There are many blue collar jobs that require a lot of education and the consequences of errors is loss of life.
I would have been incredibly rude to tell them "No, your job isn't _really_ white collar, and you haven't changed your social standing as much as you thought."
On the contrary you can absolutely be a white collar worker with low social standing in the US. It's not hard, I'd even argue most white collar workers fit that description. Think of a customer support representative working in a call center for wages. Their job is definitely white collar but it does not pay well and is the type of job you typically associate with someone struggling financially. Not someone of high "social standing".
In the US blue collar/white collar does not directly correlate to low/high social status. While it is probably true that white collar work is correlated with higher wages or salaries, it's the money that drives social status, not the color of your collar.
A friend of mine is a construction foreman. He lives in a mansion in a suburb of a suburb, is a member of a highly regarded country club and makes more money than me. He’s blue collar.
Being proud of that is like being proud of a six figure salary in California.