Not a lie, but not globally true. The price of milk and bread hasn't gone up because of extra people. Neither has the pice of gas. I know plenty of people who own their homes or have old bulletproof rental contracts that have felt the crunch of rising prices.
I finished college right at the beginning of the financial crisis. I can't overstate how bad of a state Portugal was in around 2010. There have been no jobs and no money for a long time. Since I can remember we have been the third world of the first world. Tourism and outside investment in real estate have been the one thing that's capitalised Portugal in a decade. There's been nothing else for decades.
Of course you're right that there have been economic losers from this recent large influx of people. The poorer segment especially has been betrayed by a government who opened the doors to functionally slave labour from Pakistan. There's no competing with half a million people who will pay to work if they're given a contract that allows them to stay in the EU. But that's not tourism's fault. We created our own reality.