Lead gen credit. Internet v. TV?

I am beginning to think that working on a base + lead commission is not a good idea. I'm doing work for a company that has always advertised on television. They hired me to do SEO and PPC for them, and I ended up building an entirely new website for them solely because what existed online when I got there was so bad. Now, in just three weeks after launching the new site and without doing optimization, their leads are up by 28%.

Unfortunately, we don't agree on where those leads came from. So, please help me with this scenario. Someone sees commercials for months and months, then they choose they want our service, so they go online to research. They follow the call to action and fill out a web form. The company contacts them and they in fact are a qualified lead. Then, the company asks how they heard of us, and their response is "I see your commercials all the time." Who gets credit for this lead? The same scenario can be applied with a human referral. The prospect begins to research the company online, fills out a webform or calls from the site, and turn into a lead from that research. Referral or internet credit?

My thought is that the referral and the tv were the motivator and brander, and the internet was the trigger. What are your thoughts? I have a meeting to discuss this with the company next week and would love to have some input from others before doing so.

Thanks!