Cabin air re-circulation system in 2002 Civic SI

[Filippo Librino]

I own a high mileage 2002 Civic SI hatchback. Only a relatively small number of these cars was sold in the United States. The engine is a 2.0 liter K-series K20A3.
The cabin air recirculation system does not seem to be working so well as it used to. When driving behind an old vehicle with the re-circulation system on (re-circulation button light on), I can smell exhaust gases. There is a difference, however, with having the re-circulation button off. It looks like the re-circulation door, even when in closed position, lets some outside air to get into the cabin.
An experienced mechanic (not familiar with my car, though) has told me that on most cars it is not possible to inspect the re-circulation door, without taking the HVAC out of the car, which requires the removal of the dashboard.
Does this apply to my car?
What else could be done to get the re-circulation system to work properly?
Thanks

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