I thought so. Psychiatry seems like one of those specialties where additional people viewing could only be detrimental to those types of situations.
I would agree with this for the majority of situations. For example, you will likely not be able to shadow a psychiatrist while he/she is doing any type of one-on-one work, as this will likely only make the patient uncomfortable and unwilling to share what could potentially be vital information. Unfortunately, psychiatry is a field without blood tests, biopsies or imagining equipment to assist it in diagnosing and treating patients; it is primarily based on observation and reports from the patient and family. Thus, for good reason, most doctors would not want to risk any negative impact that having someone shadow them could have on a patient's willingness to be open about what they are experiencing
There are situations, however, where you may be able to find an exception, if you are interested enough. Emergency Psychiatry, though dealing with patients in immediate crisis, does not involve as much relationship and trust between doctor and patient. As with most ER situations, the patient has likely never seen the doctor before, and will not see him/her again. Thus, having someone shadowing will likely have the least impact here, and, considering the amount of nurses and other health professionals (read: strangers) the patient would have seen in the past few minutes, you will likely not be noticed much at all. Liaison Psychiatry, which operates under similar conditions, is also an option. You may also be able to convince a psychiatrist in an inpatient setting to let you shadow him/her at certain points during his/her day, such as when he/she is just generally checking up on things in the actual unit/ward (there is usually some patient contact; but it is brief, and non-personal). As with any specialty, they will greatly appreciate any offer to do clerical-type work in addition to your shadowing; however, psychiatrists may appreciate it a bit more than others, as, though insurance companies have been known to be awful to every type of patient, the discrimination and hassle they put psychiatric patients and their treating professionals through is unmatched (and wrong, so incredibly wrong).
If you are truly interested in the field and can't find a psychiatrist to let you shadow him/her, you could always choose to volunteer (or work as a staff). What your actual responsibilities would be vary depending on the hospital; but you will generally have the opportunity to participate in room checks, escorting patients to various activities/other locations on hospital grounds, group therapy and activity, some one-on-one situations (for example: it is the staff and volunteers that are assigned to patients on constant observation status; many times, as staff and volunteers are the ones actually on the unit, distressed patients - especially child and adolescent ones - will seek them out for support/comforting; you may be assigned to supervise and try to calm down a patient placed in seclusion and restraint; etc), expressive therapies (psychodrama, art therapy, etc), attend meetings with the clinical team (including the psychiatrist) to report on how a patient seems to be doing (staff see more behavior and expressions of emotion than most anyone else, and see it more frequently) and even involvement in case conferences. You would have more say than you might assume (especially on privileges the patient is allowed to have and what level they are placed on). Psychiatry is one of the few fields where, I believe, you learn more about the actual ins and outs of the patients and diseases that afflict them by volunteering, than by shadowing a doctor. Obviously, however, the combination of experience is best.