RTLD_DEEPBIND question

I am trying to understand if RTLD_DEEPBIND should help in the following scenario 
or if I misunderstand its purpose.

There is a program that has a parser based on lex/yacc, so there is function 
yyparse in the code and global text symbol yyparse in the binary.

The program can load shared objects (plugins) using dlopen.

One of the plugins is linked with a shared library... actually with libdtrace.so.
The library has its own parser (for DTrace language) and it also has yyparse 
global text symbol.

There is a problem that when the program dlopen-s the plugin and calls its code 
the yyparse calls in libdtrace get resolved to the yyparse function in the 
program itself, not in libdtrace.
This is, of course, not unexpected according to how dlopen works.

However, I expected that if I add RTLD_DEEPBIND to the dlopen call that loads 
the plugin then libdtrace's yyparse calls would get resolved to the libdtrace 
yyparse because they all are in the same dependency subtree.

But adding RTLD_DEEPBIND does not seem to help, libdtrace yyparse calls are 
still resolved to the main binary's yyparse.

I should also note that the main binary does not have any dependency on 
libdtrace.  It comes into picture only through the plugin.

P.S.
I think that the issue could be resolved by building libdtrace differently, so 
that its yyparse is resolved at link time and is not treated as a global symbol.
And I think that we should probably do it.
However, I am still curious if RTLD_DEEPBIND should have helped here.

Thank you.
-- 
Andriy Gapon