I'd advise you to look at the charting outcomes in the match.
Independent applicants have a much lower likelihood of matching at any given # of contiguous ranked programs.
Which suggests that even if they get an interview, it is still not equal footing to US MD applicants.
This means that DO applicants need to work on maximizing their interview yield to try and maximize odds of matching ACGME.
Quite frankly this is VERY difficult to determine, because DO-specific statistics have not been published by any NRMP data I've found. Match rates for DO's have risen yearly, I think from 70% to 77% over the past 4 years (off of memory).
Furthermore the data is confounded by over 20% of those entering the match dropping out of it, likely due to matching Osteopathic residencies-- which biases the data (probably FEWER would match if they stayed in the match, as a majority of Osteopathic residencies are considered less competitive than ACGME, but this cannot be said definitively as there is no data that I'm aware of to substantiate this claim).
I'll add another layer of complexity, as the match rate only measures PGY-1, but many residencies require a transitional or preliminary year-- which many DO applicants get outside of the ACGME match-- therefore they would be considered unmatched by this tool, but actually get an advanced position (of which there are 2700 in the match currently, not an insignificant amount).
The "Independent" applicant is not representative of DO's whatsoever because they make up such a small part of that pool. 2.7K DO's in the ACGME match last year, while a total of 16.8K total independent applicants were in last years match. DO's only made up 16.2%-- a low enough rate to indicate that the match rates and number of contiguous ranks to match just cannot be extrapolated to decently represent DO's.
In terms of actual ranks-- the data shows that Independent applicants are mostly at a disadvantage at GETTING interviews. There is a stark contrast in contiguous matches in both the matched and unmatched groups in terms of US Seniors vs. Independents. US seniors, for nearly all specialties, rank double the contiguous matches.
But, and here's where it's interesting. In the rarer cases that Independent applicants do get a ton of contiguous ranks-- they match. Almost as well as their US Senior counterparts. Take as an example (purely because its the largest residency), Internal Medicine. US Seniors matched routinely, with thousands of them ranking 10 or more contiguous ranks. The odds of not matching with 10 ranks or more, was <1%. But what about the independent applicants? Well if they had 10 or more ranks? 93% chance of matching.
And again, this is not really generalizable to DO's, specifically. Although a reasonable inference to draw is if the DO match rate is MUCH better than the other independent applicants (and it is, by over 30%), then they're on much more level footing with US Seniors, once an interview has been conducted. Perhaps not level, but probably not very far off.
Where the rub lies is that they may get fewer interviews, period. And I think it's pretty well known that more than a few locations simply do not interview and/or rank DO (or other independent) applicants, particularly at prestigious or academic programs.
In my (for selfish, please-let-me-match reasons) research, I've concluded that, in general, enough interviews means you're going to match. Probably because programs are not going to interview you if they're not interested in having you be a resident, and enough ranks means even if you're low on their list, one of the programs you've interviewed at will have to get that low. I suspect that with all else being equal, many programs will take the US Senior over the DO-- but the analysis I've done indicates that DO's are not as far off as a cursory glance at the statistics may suggest.
Edit: I hope you understand I was speaking generally and cannot begin to comment on your field specifically, since I know less than nothing about it. FWIW, there are a lot of GS spots in the AOA match, although they too are highly competitive. Although participating in both matches would definitely increase the likelihood of matching, even if there is a GS-specific anti-DO bias.