"Any" press can have problems with quality because it is mass produced. I see post condemning presses that Others have nothing but praise about. So My recommendation would be to check your press for problems and if they exist, buy another brand/type and do the same test on it.
The problems that I noticed with some presses over the years was as simple as strength of materials to quality of manufacture. If you start with a weak design, you will never solve the problems. this is a case of heavy is good. Flexing of the press can be effected by where the stroke is compared to the maximum force needed to full length size big cases.
The mounting can even have an effect on the press, so the beefier the mount, the better the rigidity. If you notice in the video, when some presses are at the max force applied the entire press is moving.
Don't buy a press just because it looks good or it is recommended by a friend, study it and run it through a full cycle. If everything looks quality, strong, well designed and fit your needs, you will probably be happy with it if you properly mount it.
In many cases it is not the press that causes the problems but the dies or the procedure it's self.
I felt that the Rock Chucker supreme had problems until I bought the Co Ax and verified the problems were mine, so I modified the procedure and started doing concentricity test at each step and discovered the where and why and worked to solve them.
Now I regularly load ammo with less than .001 runout and most of it less than .0005 with ether press and my corrected procedure.
Hope all of this helps.
J E CUSTOM