It is standardly assumed that English SVO (Subject-Verb-Object) sentences are usually scopally ambiguous when both the subject and object are quantifiers.
For example, in addition to its obvious surface meaning, the sentence 'A doctor vaccinated every patient' could alternatively mean "For each patient, there was a (potentially different) doctor who vaccinated them". In what contexts would native speakers actually use such a sentence in this way?
These types of sentences are actually a little more rare than I had expected - only 25 hits total for A NOUN VERB every... at the start of a sentence in the Corpus of Contemporary American English, and 17 more if an adjective is included before the noun. Further, most of those hits were for frequency adjunct like A woman dies every 27 minutes in childbirth.
In the rest, the meaning is made clear largely by context. The following two use the construction to ascribe a property to (give a characterization of) a typical photo / resident brown.
"I provide the starting point, so they don't need the whole figure. For example, in Legs at Rest, the viewers don't need to be told there is a thigh above those outstretched legs. A photo gives every detail; a drawing gives an interpretation. A drawing is the individual experience of the artist and the viewers. If I showed all that a photo does, the drawing wouldn't be mine and wouldn't be theirs to view." (MAG: American Artist; 2002 (Jul) )
For experienced anglers, the brownie's great appeal is its wariness. A resident brown knows every inch of its home waters and it puts that knowledge to good use. It'll take you dashing beneath cut banks, around snags, and through downstream rapids. (Outdoor Life; 1996 (Mar))
This one clearly refers to several boxes each taking up a separate space.
There's too much of something, but I can't figure what it is until I spot the decorative wooden boxes on the dresser top. A box takes every flat-surfaced space: bee boxes, dragon boxes, a lady box, the hair for ring storage and compartments behind her breasts. (FIC: African American Review; 2004 (Spring))
The following is technically ambiguous, but in context it is most likely a single workbook.
Training includes a lot of practical work, including making transformers by hand. A workbook contains every key word needed for communication and instruction in Hindi, English and the language of the foreign student, plus a color-coded system. Posters in black, brown and red display different aspects of the technical work, with all three languages used here, too. ( MAG: Ms. ; 2009 (Spring 2009) )
Similarly for the skirt and blueprint in the following
At the back of the room, Esther, a Semitic siren, pushes her way to the front. A black skirt covers every inch of her sexy figure. (FIC: Hebrew Hammer, The; 2003)
Reagan had participated in planning for the funeral, which began soon after he took office in 1981. After he was diagnosed with Alzheimer's in 1994, she became the decision-maker. A 300-page blueprint set every detail. ( NEWS: USA Today; 20040614)
Of course adding in single would disambiguate the meaning.
A single thread connects every picture here: Each contains a shadow cast by the person who took it. ( NEWS: San Francisco Chronicle; 20070721)
In the vast majority of examples with a doctor, however, there is no specific referent intended.
This is an age of specialization ... over-specialization. Once upon a time a doctor treated every disease from an ingrowing toenail to double pneumonia. (Phoenix Flame, 1954)
-> Typical doctors treated every disease...
A doctor visited every cell in the facility at about 8:00 A.M. each day (Wright V. Twomey; 1974; United States Court of Appeals for the Seventh Circuit)
-> Not necessarily the same doctor, but someone who was a doctor, visited...
So I'd say that especially in the case of a doctor (did something to) every..., the default reading is not a singular doctor but rather 'doctors in general' or 'someone answering to the description of a doctor, but not necessarily the same doctor'