Many researchers are skeptical about the idea of an undocumented fight.
They fear Fleming and his supporters are merely using it as an excuse to shift the blame onto Wright for Fleming's 15 year failure to put the world's best ever germ killer to work saving lives.
I do think there was a fight and that the disagreement , in a sense, flatters Wright and diminishes a part of Fleming's current reputation (though I haste to add , Fleming himself never ever fostered this part of his reputation.)
Fleming trained as a surgeon, but never practised (supposedly).
But I think he did act and think like a surgeon, and this surgeon manque side of him coloured his whole medical career.
A surgeon's personality is drawn to the concrete and the here and now : it is specific and local by nature.
This patient is dying because of a lesion right here, not there or there or 'we don't know where or why' : let me cut it out - now ! - and they will live.
By contrast, an intellectual like Wright was a generalist, a universalizer and systematizer.
In his medical career, he focused on giving body-wide vaccines : general systemics .
He was an immunologist.
We don't ordinarily think of getting a needle in the arm of BG vaccine to prevent TB as protecting us throughout our whole body : TB hits the only lungs doesn't it ?
But TB actually hits the whole body and a vaccine against it does protect the entire body.
Fleming made his living - a very good living indeed - running Wright's highly profitably vaccine factory, but his personal scientific interests certainly display a life-long interest in locally (directly) applied antiseptics for locally-situated diseases.
His needle or sprayer he welded like a surgeon welds a scalpel.
So, back to 1929.
Perhaps Wright was merely skeptical that anything delivered merely locally to an infection will have enough oomph to kill the germs : the whole body needs to push its weight.
Wright doesn't oppose penicillin as a possible antiseptic : he merely questions the worth of any antiseptic !
(And Penicillin did turn out to be most effective as a general systemic, though simultaneous local application and even local surgery often helped as well.)
Fleming has an exalted (aka surgically-minded) and very interventionist sense of how to use antiseptics : one does not dab it gingerly around the outer edges of a wound : one gets a big needleful and drills down into the lesion just below the surface, to deliver the germ killer directly.
So in 1929, he feels penicillin might work not just by being applied to areas with germs but also may have to be injected into those areas to do its work.
One of Fleming's main competitors, Howard Florey, had wanted to be a chemist, but ended up a physiologist : he spent his entire life cutting into and cutting up animals.
It is noteworthy that he, too, found delivering penicillin as a general systemic incredibly boring and always drifted to penicillin cases where there was a surgical aspect to grab his attention.
Similarly, fifteen years later when Fleming does start using penicillin to save lives, it is this sort of work that holds his interest - not merely the putting of a needle ,every four hours, into a patient's butt to deliver a general systemic .
general internist vs local surgeons
By way of final contrast, Fleming's second main competitor, Henry Dawson, was going to be a law professor but ended up as a bacteriologist (though his main day job was as a rheumatologist ).
He was actually that rarity : a clinical investigator.
While Fleming and Florey generally never went near a patient if they could help it, Dawson was an internist, an attending physician at a big general teaching hospital.
He spent half of his day in a back room lab, like Florey and Fleming, but the other half of each day was spent on the wards, dealing with real life people with real life medical conditions.
An internist aka clinician is less focused on specific diseases as fundamental researchers tend to be.
She or he must deal with real patients who do have a specific disease, but along with this, they have a whole pile of other medical or mental conditions that greatly reduce or increase the impact of the specific disease.
Internist are biased to general systemics (and biased against locally-minded surgeons ?) such as maintaining the overall morale of the patient (aka 'a good bedside manner') and tend to view systemic medications like penicillin as perfectly in keeping with the internist's craft.
I suggest that the differing attitudes between Florey/Fleming and Dawson regarding the urgency to use penicillin as a general systemic might have been predicted from their career-long proclivities......