I see what you mean.
The following code suggests a possible workaround. Just use any suitable test image.
set display mode desktop width(), desktop height(), 32
sync on : sync rate 60 : sync
autocam off
position camera 0, 0, -200
point camera 0, 0, 0
make object plain 1, 50, 50
make mesh from object 1, 1
add limb 1, 1, 1
offset limb 1, 1, 60, 0, 0
rotate limb 1, 1, limb angle x(1,1), limb angle y(1,1)+180, limb angle z(1,1)
position object 1, 30, 0, 0
set object cull 1, 0
`set object texture 1, 2, 1 ` doesn't work on limbs here
delete mesh 1
load image "test.png", 1
texture object 1, 1
set object texture 1, 2, 1 ` but does here
repeat
sync
until spacekey()
end