How is it right-wing press spin, if it's entirely accurate as you say yourself?

"Spin" is the presentation. Calling it "uncontrolled immigration" is to put a maximally emotive framing on the subject. It's intended to trigger negative emotions and conjure up images of hordes of people arriving in chaotic fashion ("uncontrolled").

But as you clearly admit it is (was) in fact uncontrolled immigration. I think your political biases are coloring this. It's a statement of fact. You believe it's a negatively "spun" fact because it is, in fact, a negative to basically everyone. Unlimited immigration cannot work because, even putting cultural issues to one side, you can't build unlimited infrastructure at unlimited speed.

In practice there's no such as thing as "unlimited immigration". There are natural limitations such as available jobs, housing and people willing to relocate.

> a negative to basically everyone

That's a politicised absolute which is clearly false. I think your political biases are colouring this.

I go back to my previous example. The UK doesn't try to impose government control on movement between its constituent countries, and the US doesn't limit movement between states. Freedom of movement improves economic outlook.

The number of people willing to relocate to rich Western countries is effectively unlimited. Not literally infinite but so large it is equivalent. Jobs are not a limitation because governments will pay for benefits, including housing benefits. That's why it's actually fair to describe it as unlimited.

We're talking about movement within the European Union, so "willing to relocate to rich Western countries" doesn't make any sense at all. The West already includes Europe.

All EU countries are reasonably affluent by global standards. Some countries are richer than others, but it doesn't make economic sense to move from a country where you have a job to claim benefits in another one.

EU countries aren't obliged to pay benefits to people who have never worked in the country, so your idea that "governments will pay for benefits" is a very simplified view.