Problem in evaluating nested anonymous functions

Question

It seems that I have found a bug (or a fundamental problem in the design of the programming language of Mathematica) with functions defined as rules. Define the function g as g(1)=2 and g(2)=1. We can do it by

g[1]:=2
g[2]:=1

We can also define it as a list of rules by

g:=Replace[#,{1->2,2->1}]&

Indeed, when we evaluate the followings

g[1]
g[2]

after defining g using any of the two ways given above, we get

2
1

However, if we evaluate the following:

Replace[#,{{x_,y_}->{y,g[x]}}]&/@{{1,a},{2,b}}

the first definition of g leads to the following result:

{{a, 2}, {b, 1}}

while the second definition leads to the following (incorrect) result:

{{a, 1}, {b, 2}}

It seems that Mathematica gets confused when handling nested anonymous function. That is, the above Map expression is first transformed by substituting for g:

Replace[#,{{x_,y_}->{y,(Replace[#,{1->2,2->1}]&)[x]}}]&/@{{1,a},{2,b}}

(whose evaluation indeed gives the incorrect result above) and then Mathematica doesn't understand that the inner # and the outer # should be treated differently, because they belong to different anonymous functions.

Of course, this is undesirable for a functional programming language, and thus I think this is a bug.