Lobbyists are just another form of salesperson or relationship manager outside of conventional sales. Like hiring PR firms (another form of influence sales), they claim to have done shit they actually didn't do. They may have been there at the time it happened but their causal impact was nowhere near what they claim. Even when not exaggerating to get a job, these people wildly over-estimate their own impact.
The headline would more accurately be: "Candidate in competitive job interview for role in influence-sales exaggerates accomplishments and confidently over-promises future results."
(Edit to add: I was in a public company. There was no shortage of candidates (both people and firms) willing to at least imply they would or could do some fairly shady shit. We would thank them for their time and never call them back. While they may collect their fee or paycheck, my boss can go to jail and, at best, I'll only get insta-fired for even participating in the selection process, losing all my unvested options, no one-year severance/benefits.
The downside cost of even being near shady shit in a high-profile successful public company is personally catastrophic in the millions of dollars and a reputation hit to the company that wipes billions off our market cap overnight - and it only has to be the slightest bit true. Sure, you might get away with sleazy shit and get ahead one time. BUT it's not a reliably repeatable pattern and big public companies are built on real revenue and results over time. It's no different than PR. There are sleazy media outlets and/or journalists who can be unfairly influenced for $$$ but they tend to be minor league and not very valuable. At most, spending a lot on effective lobbying or PR gets you access to make your case. And often, you can spend a ton and not even get that much.)