A grand piano rests on three legs, making it impossible to have weight distribution problems; furthermore, no floor is perfectly flat or level.
A vertical piano is more prone to resting on 3 wheels; this is not good and one must ensure it is leveled somehow, not because it causes problems to the structure, but to prevent it from moving. The string tension is loaded onto the pillars at the back, certainly not onto the floor.
There are some uprights, more or less old, that rest on three wheels not due to serious flooring defects, but because over time they suffered a frame deflection due to unbalanced load distribution. An example was/is the Anelli model 30, which did not have a continuous brace on the bass section. The frame tended to flex forward on the bass part, and all those models ended up resting on 3 wheels. Even tuning them to unison was risky.
However, honestly, saying that tuning is influenced by positioning the piano perfectly level is a bit excessive. Rather, keep the humidity constant, as its variations alter the crown of the soundboard, causing the tuning to rise/fall on the central part of the plate with differences of even 2/3 Hz.
The longer the piano, the less it is affected by these variations, also in relation to the tension of the plate which depends on the design; plates with higher tension compared to the normal 70/80 kg per string are more sensitive to small climatic variations.
For example, old Ibachs had a central A that was 44 cm long instead of 40 cm; tuning it to unison is like taking, for instance, a G4 from a Steinway and stretching it until it sounds like an A4.
Here, very often people talk about tuning stability, stability, etc., in relation to the environment and the positioning of the instrument, which is certainly very important, but no one ever stops to discuss construction or design aspects regarding the type of plate, frame, lengths, thicknesses, etc..... I haven't understood if the subject is not of interest or if knowledge is actually scarce and it is more convenient to discuss the weight pressing on the leg....
In short, every piano is its own history.