Off topic, but "Turns out said DC didn't actually apply for any specialty training places as they didn't think they would be successful." is a bit unfair.
Till Streeting changed the rules to give UK medical graduates priority for training the competition was insane. Over 50% of training places were going to applicants from overseas and expensive private colleges in India were offering two year full time courses to prepare for UK specialist training applications whereas Doctors in the UK were slogging through longs and nights as part of their Foundation. Trouble is Streeting did not fully reverse Boris' opening up of the health and care jobs to full international competition. In the past many newly graduates would then take another year, perhaps as a Clinical Teaching Fellow, with regular hours and more access to research to give time to prepare for applications. Now, with no resident priority, these jobs can be hugely competitive, in part because graduates from previous years who did not get onto training are also in the pool and offering more experience.
Back to topic. @rivalsbinge suggestion is a good one. Following industry leaders and companies you are interested in on Twitter will also do no harm. If the firm checks social media, and I assume most will, there will easy evidence of a proactive interest. Part of my current exposure to the brutal jobs market is through one of my tenants who is a bright and well qualified data scientist in an area where employment is shrinking fast. One of her approaches has been to attend as many conferences as possible. Many are keen to have good attendance and indeed some countries keen to expand their financial sectors have been offering free places to overseas attendees, albeit with the cost of travel and an AirBnB. She got one place after standing behind the person chairing it in the coffee queue at another conference. Conferences and talks run by Professional and trade bodies have been another source, and often offer student rates. She has just got to final interview for a job elsewhere in Europe that has followed on from a contact she made a year ago. The year of using her annual leave to go to conferences, will also mean that she is very up to speed on what is going on in her industry.
Again anecdote but I am also hearing that several of DCs peers are very keen to move on from their first graduate jobs but can't because firms are not hiring, so are staying put, therefore clogging the career path for new graduates. And that redundances means that the pool of applicants is growing.
Is MeetMeOnTheCorner's DC a scientist? My observation is that networking does not come easily to many technically skilled but introverted scientists. And that for the roles they want this is fine. The issue is how then do they get past the filters and to interview.