This is a common and unfortunate misconception. Repeated interviews going badly and/or repeated failures to get a job can make someone specifically anxious about job interviews. Also, let me explain some of the crucial ways the job interview experience is distinct from work experience:
1) In an interview, you can lose the job at any moment for any little reason, because you don't even have the job yet, whereas on the job you're very unlikely to lose your job at any moment for any little reason. It typically takes gross incompetence or insubordination to get immediately fired. I've written plenty of software bugs in my career, as has everyone I suspect, but I've never been fired. I've lost plenty of jobs in interviews though.
2) The stakes are personally higher in a job interview, especially if you're currently unemployed. You can claim theoretically that the stakes are higher on the job, because "millions may be lost", but those aren't your millions, they're the company's millions. The company losing millions may suck for the company, but it doesn't necessarily mean you lose your job. Companies lose millions yet continue in business. Whereas if you don't get a job at all, you'll eventually run out of money and become homeless. That is the highest of stakes, for you.
3) If you've had a job for a while, then your coworkers already know that you're competent. They aren't suspicious of you or sitting in judgment of you, because your work has already been seen and judged. Whereas in a job interview, it is a stranger sitting in judgment of you. The issue isn't necessarily "talking to strangers" but rather you have a stranger who is wondering if you're a "faker who can't code your way out of a paper bag", and you have to prove to them otherwise in an hour.
4) In a job interview, someone is standing over you watching your every move while you work. Unless you do pair programming (which I dislike), most programmers are sitting alone at the computer most of the time, not having someone else stand over them. And even if you do sit with a coworker at the computer on the job, the process is usually collaborative rather than judgmental. You and a coworker sit together to solve a programming problem together, not so that your coworker can judge you and give you an evaluation which determines whether you get paid or not.
5) The tests given in job interviews are usually totally artificial and often have nothing to do with the job. You're just given a test — sometimes ill-defined — out of left field, at the spur of the moment, and you have to solve it in a few minutes, because the job interviewer can't sit and wait for you to take however long you need. People who interview a lot, or who are coached in interviewing techniques, apparently learn that there are tricks to interviewing, and you can ask the interviewer multiple questions to clarify and talk through the process, but someone who doesn't interview much doesn't know this. You rarely get such artificial, out of left field problems at work that need immediate solution. At work, you have meetings, discuss the product, discuss what's needed, before you work on things. Or if there's a work "crisis", the crisis has to do with your company's codebase, which you're already familiar with and may have written yourself!
I could go on and on and on, but hopefully that's enough to show that the pressures of job interviews are unique and not the same as work pressures, no matter how bad the "emergency" at work.
One more thing about different pressures and psychology: It's well known that many people have a specific fear speaking in front of groups of people. So why is the notion so strange that people have a specific fear of job interviews. I have little doubt that there are firefighters, who rush into burning buildings for a living, who would feel sick at the idea of giving a speech in front of a thousand people in a non-burning building. Anxieties are not all the same, they're often very specific.
It's sad to me, though not surprising, that many hard techies don't understand human psychology and have a hard time empathizing.