I can't speak for Elizabeth, but I interpreted that part of her reply to be in regards to how you said this mama was planning a hospital birth. I took it more as 'well, she was posting in the UC forum' So therefore replies will be from a UC perspective not a 'you have to go to the hospital and have birth assistants' perspective.
Additionally, not that I'm a total purist or anything, but to have or not to have a doula at a UC does sort of raise questions about contradiction in terms. I realize that UCing varies from person to person in who they want there, and that doulas are not intended to be medical personnel, but they are hired as attendants to the mother. This would be very different from a mother going solo, or just having her partner and/or children present, or even having a close friend or a mother there, etc.
Doulas are hired professionals. In this sense, and from a (or at least one typical) UC perspective, this would be seen as potential "intrusion". And please, don't be thrown or offended by the word "intrusion"... it's just the way it is, and I can't think of a nicer word for "intrusion". I basically just mean the presence of outsiders or hired hands during a birth (i.e. "strangers").
Any doula may or may not take this personally, but consider that it's because this is your vocation. We are not a threat to you in questioning whether we or other women need you during labor. You don't have to feel so challenged by these suggestions. Especially not if such notions are brought about in the UC forum, of all places.