There is a lot data that points to Ballantine being the source of Bry 96, starting with Siebel's catalog description of the yeast strain.
https://www.siebelinstitute.com/products/liquidbrewingyeast/bry96/"This is a flocculent top fermenting ale yeast from a brewery formerly operating on the East Coast of the United States. It produces a very clean ale flavor which has been well accepted in a number of breweries."
Sierra Nevada acquired "Chico" from Siebel as Bry 96. The yeast propagators acquired the strain directly from Sierra Nevada or indirectly from another propagator.
Now, it is well known within the research community that sequential accession numbers within a culture collection are often from the same source, which means that Bry 97 could be from the same source as Bry 96.
If that knowledge is not enough data to seal the case, G.W. Lange deposited two Ballantine deposits into the USDA ARS NRRL collection:
NRRL Y-7407 (Siebel BRY 96)
Accession numbers in other collections: Lange 2
Isolated from (substrate): BR, Beer pitching yeast
Substrate location: Ballantine Brewery, New Jersey, USA
Comments: ID from 26S renal partial sequences.
NRRL Y-7408 (Siebel BRY 97)
Accession numbers in other collections: Lange 4
Isolated from (substrate): BR, Ale pitching yeast
Substrate location: Ballantine Brewery, New Jersey, USA
Comments: ID from 26S rDNA partial sequences

Did you notice that these deposits were made in the same order as Bry 96 and Bry 97? In my humble opinion, that ordering is not a coincidence.
Finally, here's a photo of Ballantine's ale culture at work:

That strain is definitely not Bry 96. It is a true top-cropping strain. Bry 97 is a true top-cropping strain, which why Brulosopher had a blow out.
So, here we have a lot of facts that point to Bry 96 and Bry 97 having originated from the same source.
Fact #1 - G.W. Lange deposited two different Ballantine cultures into the NRRL collection (both of which are Saccharomyces cerevisiae); hence, we know that there were at least two Ballantine yeast cultures.
Fact #2 - Culture #1 (Y-7407) is cold tolerant enough to produce a psuedo-lager. Bry 96 exhibits excellent cold tolerance for an ale yeast, which points to its use in the old Schalk Brothers plant.
Fact #3 - Siebel lists an East Coast brewery as the source of Bry 96. That source has long been known to be Ballantine.
Fact #4 - Sequential accession numbers are often from the same source, and the deposits appear to be in the same order in both collections.
Fact #5 - The ale strain employed at Ballantine was a true top-cropper as can be seen in the photo shown above. Bry 97 is a true top-cropper.
Fact #6 - Here's a fact that even most professional brewers do not know; namely, production ale strains tend to be polyploids (more than two sets of chromosomes). Bry 96 is a diploid yeast strain
1, which is rather rare when it comes to brewing yeast strains. What I have found in my studies is that at least two different breweries used diploid S. cerevisiae cultures to produce lager beer. The other brewer was the defunct Acme Brewing Company in California. This strain is available as U.C. Davis Phaff 40-219.
[1] Labeled yeast number GSY 708 in the following publication:
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC2556262/pdf/1610.pdf