In the articles on tribes in Insight on the Scriptures (volume 2, page 1125) there is the following explanation:
Tribes of Israel. The tribal arrangement in Israel was based on descent from the 12 sons of Jacob. (Ge 29:32–30:24; 35:16-18) These “twelve family heads [Gr., do′de?ka pa?tri?ar′khas]” produced “the twelve tribes of Israel.” (Ge 49:1-28; Ac 7:8) However, Jacob blessed Joseph’s two sons, Manasseh the older and Ephraim the younger, and said: “Ephraim and Manasseh will become mine like [his actual sons] Reuben and Simeon.” (Ge 48:5, 13-20) When the various tribes received their land inheritance in the Promised Land (Jos 13-19), there was no “tribe” of Joseph. Instead, “the sons of Joseph,” Manasseh and Ephraim, were counted as distinct tribes in Israel. (See BOUNDARY ; MAP , Vol. 1, p. 744.) As Jehovah had arranged, though, this did not increase the tribes of Israel receiving an inheritance to 13, because the Levites got no land inheritance. Jehovah had chosen “the tribe of Levi” (Nu 1:49) in place of the firstborn of the other tribes to minister at the sanctuary. (Ex 13:1, 2; Nu 3:6-13, 41; De 10:8, 9; 18:1; see LEVITES .) Consequently, there were 12 non-Levite tribes in Israel.—Jos 3:12, 13; Jg 19:29; 1Ki 11:30-32; Ac 26:7.
Towards the end of that page, and continued on the next, we find a section that talks about the tribes of the so-called "spiritual Israel":
Tribes of Spiritual Israel. Revelation 7:4-8 divides the 144,000 members of spiritual Israel into 12 ‘tribes’ of 12,000 each. (See ISRAEL OF GOD .) The list differs slightly from the lists of Jacob’s sons (including Levi) who were the tribal heads of natural Israel. (Ge 49:28) The following may be the reason for the difference:
Jacob’s firstborn son Reuben lost his right as firstborn by his misconduct. (Ge 49:3, 4; 1Ch 5:1, 2) Joseph (the firstborn son of Jacob through his second, but favorite, wife Rachel) gained the privileges of firstborn son, including the right to have two parts, or portions, in Israel. (Ge 48:21, 22) In the Revelation list “Joseph” evidently stands for Ephraim. And Manasseh represents Joseph’s second portion in spiritual Israel. The tribe of Levi is listed; to make room for Levi without increasing the number of tribes, no tribe of Dan is included in Revelation 7:4-8, but apparently not because of any unsuitability on Dan’s part. The inclusion of Levi would also serve to show that there is no special priestly tribe in spiritual Israel, the entire spiritual nation being “a royal priesthood.”—1Pe 2:9.
I think this information explains perfectly the position held by the Watchtower Society.