Not sure how it relates to your point, but in the examples you have there the distance differs in both examples. I think the most relevant comparison is between situations where the subject distance is identical. It still makes sense to me that in that case, only the aperture matters. But could you provide the name (Or link if it is online) of the tool you're using there?
The idea is this, most of the time long tele lenses are used to get an acceptable subject size, if the lens is too short (a 400mm) then a longer lens is preferable (a 700mm), but if the 400mm is used either because they didn't have a 700mm etc then people invariably crop the 400mm to get the subject the same size as the 700mm, even if they crop that 700mm they still crop the 400mm even more to get the same framing/subject size.
Now the statement was that
"At f8 700mm, your depth of field will be shallower than a 400mm lens at f4. Focul [sic] length has a much greater affect on DoF than aperture." followed by
"That is true" my point was it isn't true.
So imagine two shooting situations:
1: Two photographers 20 meters from a bird, one has a 700mm f8 the other a 400mm f4 both on the same model camera. The person with the 700mm f8 doesn't need to crop but the person with the 400mm has to crop to get the same subject size. The 700mm f8 has a dof of 0.38m, the 400mm f4 has an initial pre crop dof of 0.59m but after the necessary crop it is approximately 0.35m.
2: Same two photographers, the guy with the 400mm lens is closer to the bird by a factor the same as the focal length difference so when they both take an image the bird is the same size in the image without either cropping. Say the 400mm guy is 10m from the subject, he has 0.12m dof, meanwhile the 700mm guy would be 17.5m away and have a dof of 0.18m
In both real world scenarios the 700mm f8 has greater NOT shallower dof than the 400mm f4.
I just googled a dof calculator and clicked on the first one that came up.
https://www.photopills.com/calculators/dof