it seems to be that a left b inner c:

a --> b <--> c

a has 5 rows, 1,2,3,4,5
b has 3 rows, 1,3,5
c has 3 rows, 1,2,3


a --> b generates:

a1, b1
a2, null
a3, b3
a4, null
a5, b5

b <--> c added:
a1, b1, c1
a3, b3, c3


So yes, INNER JOINing a table, to a table that was outer joined, flattens the OUTERness of the join, by removing any null columns

To work, it must be:
a --> b --> c