I am sure the nurse means this question as bright and breezy, perhaps inviting the response "We are (more likely "I am") fine, thank you." However, it is hard to avoid the suspicion that there is an element of condescension here, mirroring the fact that the nurse is up and bustling around, while the patient is lying passively in bed. What is actually going on in this question? Are there other circumstances in which someone can be addressed in the first person without any connotation of condescension?
The use of “we” to indicate the singular has three forms, the first two of which refer to the first person singular:
The first, used by rulers dates back to at least the 13th century:
1854 W. M. Thackeray Rose & Ring xv [The herald]..began to read:—‘O Yes!..know all men by these presents, that we, Giglio, King of Paflagonia’ [etc.].
1987 M. Thatcher in H. Young One of Us (1990) xx. 491 We are in the fortunate position..of being..the senior person in power.
The second is even older. It is used to create an impersonal style and tone, or to avoid the repetition of ‘I’.
1965 S. Lipschutz Outl. Theory & Probl. Gen. Topol. iv. 47 We assume the reader is familiar with the geometric representation of R by means of the points on a straight line.
2003 N.Y. Times 2 Mar. 11/4 The commander of American forces..has backup plans for moving American forces into Northern Iraq. ‘General Franks, as we speak, is looking at lots of options.’
The third version is the version in question:
1 f. Used confidentially or humorously to mean the person or persons addressed, with whose interests the speaker thus identifies himself or herself (esp. by a doctor in friendly or cheering address to a patient); also used mockingly or reproachfully by a parent, intimate friend, etc.
1702 J. Vanbrugh False Friend i. i. C 3 Well, old Acquaintance, we are going to be Married then?
1756 T. Gray Let. 21 Sept. in Corr. (1935) II. 481 We [sc. Chute, who had been ill] have been up a second time for two days in our Chair.
1973 G. Chapman et al. Monty Python's Flying Circus (1989) II. xxxvii. 199 Doctor Morning, Mr Henson... How are we today?
1992 B. Keenan Evil Cradling xiii. 178 The words that his mother had spoken to his father when his father got angry about something. ‘Now, now, we are getting very paddy today, aren't we John?’
Note the 1973 quote. This marks the point at which “we” is now being used as satire by recognising the blurring of the line that has already taken place between a “friendly or cheering address” and the condescending “mockingly or reproachfully” and overly familiar nature of such use.
It is probably a marker in cultural shift that recognises the annoyance felt and created by a formulaic device with more than a little transparent insincerity.
It also marks a change from an attitude of respecting professionals for their status to respecting people for their abilities fostered by a general feeling of equality and a general entitlement to respect.
The answer to the question of "When it is permissible to use this form?" is probably "Never."
Sharing a different perspective. We nurses, generally and one would hope, have a sense of empathy for those to whom we provide care. When the hypothetical nurse in this question asks about "we", I feel that sense of empathy communicated rather than condescension. "We" are working together for your progress towards a better state of health, not you alone. If "you" are not feeling well, then "we" are not feeling well, which honestly does affect how I feel.
From an organizational perspective, employees work as a team towards common goals. I might perform some work, write a policy, research some knowledge for a project, etc. But I feel unease at taking implied credit knowing that all of the work is a team effort so I say "we" quite often, even when referring to my portion of the effort. My belief is that team cohesion is strengthened when we use inclusive terms.
Additionally, "we" implies authority greater than "I". As one who frequently must remind others of organizational policy and state and federal regulations, I say "we" and "our" to make clear that these are not my personal rules, rather my reminder is backed up by the organization or even the federal government. Also implied is, again, inclusivity in that "we" are held to such policy and regulation, not just the individual to whom the reminder is directed.
Reading the question and answers was enlightening of the differing perceptions. Perhaps my career and work culture contribute to my perception of the question, and apparently it is not as general a perception as I had thought. Communication is a wonderful tool for understanding cultural differences.