I only have a second-hand experience with PhDs looking for jobs. It seems very similar to programming jobs market: it's saturated with worthless applications and the filtering on the receiving end is completely broken. I don't have numbers and wouldn't know how to measure it, but it feels like most applications never get assessed by relevant experts at all. Basically, no matter what you put in your resume it goes straight into the garbage bin.
So, your professor's rules are no longer relevant. There's nobody to speak to, no matter what you write it's not going to change anything. Thinking isn't a priority either.
You need to know people. That is all.
Anecdotally, I had this happen to me. For the context, I'm moving back from the Netherlands to Israel. I've been looking for a job in the Netherlands before giving up and leaving. Despite maybe a hundred or so applications that I've sent, I've never heard from anyone. I think, Dutch law requires a timely response to the application and so I would get template rejections most of the time. Sometimes seconds after applying.
Back in Israel, I also applied through LinkedIn and Indeed. But I also happen to be on the file in some HR agencies which supply candidates to the programming jobs. I've received an invitation from such an agency to interview for a job with a company I've already applied to through LinkedIn (and was promptly rejected). I've landed an interview, and when asked about my job hunting efforts in the Netherlands, I jokingly described the application through LinkedIn and the likes as futile, as nobody reads those applications.
The interviewer start beating his chest assuring me that they would never... I decided to withhold from them the fact that they actually would. I'm still at the... third interview with them now. So, we'll see how it goes.
Anyways. My larger point is: the automation brought to job hunting is very disadvantageous to the junior workforce. Connections always played a role, but now their role is exaggerated. The article describes it as decreased job mobility (nobody quits, so there are fewer jobs to hire people into). And while it keeps the appearance of low unemployment, the problem with it is that it's the same people who are unemployed all the time. Our unemployment model isn't prepared for this. The idea behind social security unemployment compensation is that you find a job relatively quickly and only need a few months to get by before you do. This doesn't work anymore, as unemployment lasts years.
This is bad on many levels: it lowers the number of professionals entering the field, it leads to the loss of expertise as older workers retire w/o having trained a replacement, the effort spent on acquiring expertise is wasted by the young workforce as they are forced to change direction.