The compiler, including the current latest version (16, update 1), doesn't raise an error with the following code:
module m
implicit none
private
type, public :: t(K)
integer, kind :: K
private
integer(kind=K) :: I
end type t
end module m
program p
use m, only : t
implicit none
type(t(K=4)) :: foo
foo%I = 42 !.. I is a private component of t
stop
end program p
1>Compiling with Intel(R) Visual Fortran Compiler 16.0.1.146 [Intel(R) 64]...
1>m.f90
1>p.f90
1>p - 0 error(s), 0 warning(s)
