You don't think the UK Government could have done more to support the UK Steel industry? It's quite a complex issue isn't it and whilst the EU rules around state aid no doubt didn't help, the UK government could have done a lot more e.g. lowering business rates.
The closures were fairly inevitable due to the significant loses they were incurring caused by lowered steel prices due to global imports, with Russia, South Korea and particularly China cited as dumping steel. Other factors mitigating against profitability included high energy costs (including green taxes), high business rates and oversupply/low demand. In addition the UK government had voted against increased tariffs on imported Chinese steel due to its free trade policies, limiting import duties to minimal amounts (around 10%). The Daily Telegraph reported that the UK Government's failure to back EU attempts to increase anti-dumping measure on imported steel had been the tipping point in Tata's decision to exit the UK steel business.
Re your second paragraph, the lower steel prices equally applied in the Netherlands. And the EU Green Taxes also applied in the Netherlands. As for the UK not backing EU tariffs and quotas on China dumping steel, the UK can't block an EU wide tariffs and quotas.
Could the UK govt have done more? Without a doubt, but the climate for Tata to move was already there, and the decision to move was made long before China started dumping. The story is complex, including over £600m paid to Tata in carbon credits for mothballing the plant whilst the new one in the Netherlands was being built. The whole story in long and complex but the fact remains the EU have a criteria for attracting business into the EU, and one of those criteria is that it doesn't mean losing jobs elsewhere in the EU. If you look on the EU's own site it shows the investigation that took place re the funding and the move, and its a whitewash. Similarly the EU carried out one for the JLR move to the Czech Republic... another breaking of the EU's own rules and another whitewash.
Taking it back to your original point, I have every sympathy for the workers that lost their jobs whilst the EU flouted its own rules in funding and subsidies. Those weren't the scare stories you spoke of but are real hard, fact based stories. Many people in the NEast, where heavy industry has been decimated know that their job was shipped to the mainland EU with the help of the EU. They were never going to vote Remain.