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I use this code here:

mat = bpy.data.materials.new(name="Red")
tex = bpy.data.textures.new("red", 'IMAGE')
img = bpy.data.images.load("D:\\red.png")
tex.image = img
slot = mat.texture_slots.add()
slot.texture = tex
for obj in bpy.data.objects:
    obj.select = True
    bpy.context.scene.objects.active = obj
    obj.data.materials[0]=mat
    mesh = obj. data
    face_list = [face for face in mesh.polygons]
    for face in face_list:
        face.select = True
    bpy.ops.object.mode_set(mode='EDIT')
    bpy.context.tool_settings.mesh_select_mode = [False, False, True]
    obj.active_material_index = 0
    bpy.ops.object.material_slot_assign()
    bpy.ops.object.mode_set(mode='OBJECT')
    obj.select = False

enter image description here Then I switched to 'Texture Paint' Mode. And I found only the last mesh I processed was shown painted. I want them all painted.

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Can set the material directly with obj.active_material. The material index will be obj.active_material_index. The material can be set directly to the faces with face.material_index. Note I've used the scene.objects collection, and only looked at mesh type objects.

Test code below.

Textures fine, commented out re filename.

import bpy

context = bpy.context
scene = context.scene
#  reuse Red material
mat = bpy.data.materials.get("Red")
if mat is None:
    # create
    mat = bpy.data.materials.new(name="Red")
    mat.diffuse_color = (1, 0, 0)
    #tex = bpy.data.textures.new("red", 'IMAGE')
    #img = bpy.data.images.load("D:\\red.png")
    #tex.image = img
    #slot = mat.texture_slots.add()

mesh_objs = [o for o in scene.objects if o.type == 'MESH']

for mesh_obj in mesh_objs:
    mesh_obj.active_material = mat
    mesh = mesh_obj.data
    for face in mesh.polygons:
        face.material_index = mesh_obj.active_material_index
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