Both the upper and lower tank(s) will be supported entirely by nails or screws in shear, unless you used glue for all joints. Even then, it would be much safer if there were legs under the rectangular frames.
You are correct in that they are supported by the nails. The framing nails used have a shear strength somewhere in the 200-300lb range.
Water weighs 8.3 lbs/gal and each rack will have 20 gallons for a total of about 166lbs per rack. The four support legs on each rack should evenly distribute the weight which gives us 41lbs/support leg. Each one was nailed 3 times. Assuming the weight is shared fairly evenly by the three nails on each support... it means that each nail is only supporting about 13lbs.
13lbs per nail is well within their shear strength and even further in my comfort level.
Most stands are built considerably less sturdy. Here is the 30 gallon stand next to the rack. It appears to be a particle board instead of solid lumber like I used. The particle board is 1/2 or 3/4" thick and similar to my construction in that it relys on the shear strength of 2 bolts/side and the vertical legs are not under the horizontal base. It has been holding strong for 10+ years.
You're correct in saying that it would safer if the vertical legs sat under the rack to support their weight directly but it would also be safer to wear a bullet proof vest and helmet 24/7. Some redundancies aren't necessary...