If you are in the US and a usual area for growing cane fruits your State Extension Service should have good information about this

Boysenberries are a cross between a raspberry, common blackberry and a loganberry. They share the growing characteristics of a blackberry or loganberry (also a raspebrry/blackberry cross) more than that of a raspberry so any training or pruning instructions for blackberries would be appropriate.

Accounts of the parentage vary:

https://www.bing.com/search?pc=COSP&ptag=N1140D060418AE20BDC3E2E&form=CONBDF&conlogo=CT3210127&q=boysenberry+parentage

They may "vary" in publication as you allude but the parentage I quoted was taken directly from the originator, Rudolph Boysen in northern California. Mr. Boysen never took the berry to market and he sold his farm and it was allowed to go fallow. Hearing rumors of these large, sweet reddish purple berries, the vines were salvaged and rescued from the abandoned farm by George Darrow of the USDA and Walter Knott, a berry farmer in SoCal and transplanted to his farm in Buena Park. Knott began selling the berries he named for their originator at his berry stand in 1932.....which later became known as Knott's Berry Farm.

Boysen parentage was a topic of discussion at last summer's Caneberry Field Day at NWREC. The subject was triggered by a farmer's lawsuit against a grower that supplied an incorrect strawberry cultivar, as proven by genetic testing. Boysen was chosen as a topic example because it has been assumed all Boysens are the same strain when in fact various offerings are all over the map DNA-wise. The truest strain was considered to be plant material collected recently from Mr. Boysen's grand-daughter in California.

Christie: Boysen berry canes are a trailing variety. The canes stay somewhat thin and flexible and are easy to train if gloves are used. The canes tend to grow very long without forming laterals (branching). In commercial plantings, several canes are bundled together, sort of like a wreath. Fruit will form all down the cane, regardless of how long it grows.

Follow general guidelines for blackberries: remove canes that have fruited after harvest is done and train canes that grew new for the current year in the old pruned-out canes place. The trick is to keep the new canes separate from the old until the post-fruited canes are removed. Because of the thorns, it would be difficult to separate new from old if allowed to closely mingle.

>They may "vary" in publication as you allude but the parentage I quoted was taken directly from the originator<

If you look at hits on the page I linked to the version you give is present. With the important difference that a known parentage was not obtained along with the plants being rescued. With the result that genetic analysis has been used since to try and figure it out. Something that is not cheap, would not have been undertaken if there was information available that was considered reliable.