Welcome to a vigorous discussion! I am a senior radiologist, and have heard this prediction any number of times from fellow radiologists, as well as other doctors, some of whom were competitors from other specialties.
Radiology, like any medical specialty, is subject to change. When I joined radiology, a lot of my IM colleages felt I was making a bad decision, throwing my lot in with a bunch of misfits who worked bankers' hours and made too much money. Fortunately, my reasons for becoming a radiologist had nothing to do with remuneration or workload, because I have never belonged to a 'rich' practice (e.g. one where partners make >= $600K/yr.) and have never in my career worked less than 60 hours a week and sometimes much more. I freely admit that some of my associates in various locations I've worked fit the stereotype more than I, but nearly all of them burned out early and are now retired or doing something less strenuous. The fact is, in order to do radiology well, you have to LOVE it, because only LOVE will enable you to deal with the radiologist's burden, which includes all of the following difficulties:
1. Building and maintaining a team of technologists (who make the images you interpret), receptionists, nurses, and managers, while developing mutual trust and regard which makes teamwork possible (hopefully inevitable). If you can't get along with other people from many backgrounds, forget about being a radiologist.
2. Establishing credibility with skeptical and sometimes competitive referring physicians through dedication to serving them and their patients, and caring about them and their practice difficulties.
3. Working with patients who are simultaneously scared of radiation, nervous about the results of their examinations, irritated by any delays or difficulties in their care, and fascinated by the technology your department commands.
4. Dealing with the inevitable malpractice suits. Since radiologists are currently involved in the care of most patients, if something goes badly wrong, it is certain that the radiologist will be named in the ensuing lawsuit. The worst part of this is getting sucked into a settlement when you, your defense attorney, and sometimes even the PLAINTIFF'S attorney agree that you were really not responsible for the bad outcome, but just involved in the wrong case. (This doesn't happen often, but this DOES happen, believe me.) Learning, hopefully, that the law is about WINNING, but also about compensating patients with a bad outcome, and still trying to do what is right. Learning as well that lawsuits (unless you really screwed up) have little to do with your value as a physician, and should NEVER be taken personally. (Some of these lessons apply to all physicians, not just radiologists, of course.
4. Attending meetings, reading papers and journals, pounding the WWW, for the latest information about image interpretation and technology.
5. Dealing with hospital administrations that are extremely variable in competence, honesty, and willingness to solve problems, and frequently hostile to radiologists and sometimes to physicians in general. Learning that a good administrator who is fair, willing to help and who likes you is a pearl beyond price (and fortunately not all that rare).
6. Constantly educating your fellow physicians (including those who do NOT refer) about your capabilities, limitations, and service availability, to enable them to most easily and effectively use your services.
7. While doing all of these other things, interpreting an unending stream of images, sometimes thousands of them per exam, and doing your darnedest to miss no significant finding (nearly impossible), answer the questions posed by the referring physician, and turn the raw data of the images into information (data with significance) that will make a difference in the care of the patient. Carefully compiling this information into a report that is concise, easily readable and unambiguous.
Usually generating the report, using balky continuous speech recognition software that can, if your weary eyes don't catch it, insert misinformation, disinformation or utter nonsense into your report.
So why should radiologists exist? If they add little or no value to patient care, they shouldn't. However, most radiologists add a LOT of value, even when they are NOT good at all the activities described above. Do not think that because other docs discuss the images without mentioning the report that they would ever consider IGNORING the report, unless their local radiologists are complete klutzes (a most unlikely situation in any academic locale). It is possible that the local rads are not friendly (slightly more likely in academe, I am sorry to say), or the reports are too delayed by bad management of the radiology workflow (hardly ever the fault of the radiologist and usually due to really BAD administration) to be useful on rounds.
I also add that doing all radiology via tele-imaging has been tried, and doesn't work well. There is no substitute for direct physician to physician interaction when difficult cases are involved (and radiologists see all of these sooner or later) and it is nearly impossible to do this effectively remotely, even using video conferencing. So, the idea of all radiologists working from home (an abomination--it is much MUCH better to be where the action is, and better YET to be able to see, talk to, inform, and comfort the patient) or from a beach in Sri Lanka is an idiotic pipe dream. Where teleradiolgy is useful is in providing emergency coverage and temporary readings in order that the local radiologists can sleep at night. And, if you think there will be no USA jobs for radiologists in the future, consider who will be asked to handle after hours teleradiology for India and China (3/5ths of the world's population) when their medical technology catches up and THEIR radiologists need a good night's rest. I hope by that time that schools will teach Hindi and Chinese, so that we'll be able to communicate with our overseas colleagues! Teleimaging is also useful for inter-radiologist consultation, which will assume a much larger role in the near future.
As I write this, the US job market for radiologists is not good (I can state this with great authority, since I have been searching for my next adventure for over a year now). However, in radiology, an apparent job shortage can turn into a tremendous job market very quickly, since in bad times radiologists on the verge of retirement tend to hang in to help their practices, and then depart en masse when the crisis is over. The current uncertainty about payment from Medicare et al, as well as the bad general economy, has created a crisis mentality in the specialty, and, once conditions become more stable, that will dissipate.