Yes, Doxygen has a parser for Fortran. That's exactly my point - it has a complete parser, not just a filter. If COBOL were sufficiently close to C, it might be possible to create a Doxygen filter for it; but it isn't. Creating a Doxygen parser is a lot more work than creating a filter.
It'd be great if there were a Doxygen parser for COBOL, but it's a big task, especially given COBOL's variety of incompatible source formats. Just handling both procedural and OO COBOL would be tough. (The last time I looked, Doxygen's PHP parser didn't correctly handle some mixes of procedural and OO PHP, and the COBOL situation is even harder.) As always, the problem is finding someone who has both the necessary knowledge and the time.
I suppose it might be possible to adapt the parser from, say, OpenCOBOL, and at least handle procedural COBOL in Doxygen. I haven't looked at the OpenCOBOL sources to see how plausible that might be.