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This challenge resides not with v or t, but with d. I propose that x' = x - d is wrong and so consequently substituting vt for d will be wrong too.
Additionally the inherent transformation difficulties has nothing to do with time, velocity, light, observers, or any other such physical considerations as this is a challenge solely based upon mathematical princples havving been broken.
from Wikipedia...."coordinate transformation"
S 2 3 4 5 6 vt 8 9 10 P abs P = 11. s' 1 2 3 P' abs P' = 4. einstein. s 2 3 4 5 6 4 3 2 1 P' abs P' = 11 -7. real coordinate transformation. s 2 3 P' 5 6 s' 8 9 10 P abs P = 11 abs P' = 4. P' int diagram  the following chart suggests that x' does not equal x - vt One point P... in one frame erroneously gets assigned two different coordinations. Call that point either x or x' or P...it is but one point in S and can have but one and only one coordination allowed per point.. 1 the point x in S is at ( x, 0 ) 2 the point x' in S is at ( x-vt, 0 ) This establishes the equation... x = x - vt which obviously is only correct when t = 0. This is done by Einstein's mathematical sleight of hand ! His allowance of a second coordination for the same point in the same frame, is cloaked in deception, and has traditionally been very, very difficult to spot. Indeed motion as well as time can be ignored, by letting VT = D, [ Velocity times Time = Distance ] and still the inequality persists. X = X' + D, since once again, point X' in S is point X is point P. He neither tranforms a point nor a coordinete...indeed he transforms a mere line segment length into S. This x' distance in S must begin from the origin and not be counted off backwards from point P.  some of other attempts to document Galilean challenge- traditional style other attempts to document Lorentz challenge- time dilation original poem Miles Mathais's challenges to x = x' + vt |