You can counter this by showing what you can do and how you can help them right at the start. Bring your laptop and be prepared to show code samples, demo applications, documentation, training materials or whatever you else you can and jump on any opportunity to take charge and show your stuff. Try and promote a feeling of optimism and the sense that you take pride in your work.
If you get the chance to chat, ask about something they'e struggling with and relate that back to your own experience. Tell them about your struggles, how you kept your head and helped the team when things got tough and make sure they know how happy it made you when you finally shipped your last product. Real craftsmen will know what you're talking about and appreciate it.
Finally, do your research before you visit. If you can, ask for the interview schedule in advance and find out what you can about your interviewers.
This has almost always paid off for me. At one job I discovered one of my interviewers studied under Knuth. Early in the conversation he asked if I had any questions and I immediately jumped on that, asking him what it was like to work with him. He smiled and said that the hardest part for him was the effort he had to put into TeX and typesetting.
Be honest as possible, but know when to not be too honest. Don't go detailing how you systematically helped the previous company you worked for spiral into bankruptcy or how you never got along with your boss. There is a line, answer their questions, but don't go into too much detail unless asked for it (it's rare an interviewer wants copious amount of detail).
On the honesty front, don't be afraid to embellish your experience and back story slightly either, but ensure that it's manageable embellishment. Because if you go claiming you have these amazing skills and they find out you don't, you'll be sent packing quickly and it'll be embarrassing for you.