I work in the UX team for a major online retailer in the UK. We spend a large part of our time testing and validating our designs with real customers - not much goes live without us being sure it's the right thing. If something doesn't work for people, even if we think it's great, then it's gone.
How many times has that actually happened though? I talk to designers all the time who say some variation of this but have literally never done any of those things.
Depends on the task, but if it's for a big project we'll go through multiple rounds of usability lab testing before a design gets built.
Then, after launch we'll do rounds of optimisation based on the data we get back. This bit doesn't happen as much as we'd like as newer projects take priority, but it does happen and we're working on ensuring the Build > Measure > Learn loop is an integral part of the process.
We're lucky as senior management understands the benefit of testing and iteration. One place I used to work, the chief exec thought they knew everything, so didn't understand why we wanted to research and test stuff all the time. So we ended up having to do what they wanted, rather than what we knew the customer needed.