Yes this is regularly the case. Not an urban myth I am afraid
Patients, sorry clients, are admitted into mental health units in various ways from voluntarily to a range of provisions- aka Sections- under the Mental Health Act. They are assessed and a individual care plan is written. It is at this point that I and others would like to see the issue of arson/facination with fire, assessed and if necessary, addressed.
In some Hospitals/Units, it is often only the most ill who have smoker's materials removed from them. However, as they share facilities with other patients on lesser restrictions, cigarettes- and more worringly, matches & lighters can be freely swapped between them.
I have been involved with a number of Mental Health Units. Very few routinely search all patients. Mainly only those who have forensic wings. Some Trusts are proactive and ban lighters/matches but provide non flaming cigarette lighters (similar to those found in cars)to control the risk
Some Psychiatric Consultants and other professionals use the human rights angle to justify this approach, while the nursing staff on the unit moan about the extra work searches involve using the "It's not a Prison" argument.
As a result, cigarettes, matches - and my pet hate - disposable lighters- are routinely held by even the most vulnerable clients.