If they do a bad job at creating and servicing products which draw people to the site, people will not go there and Google will not make money. So, is gmail 'not a product'? No, that's absurd.
I've worked on Google Search for several years, and I can assure you that neither I nor most colleagues I know see things this way. I can't think of a single example where our search results have changed or not changed based on how it would affect Adwords customers. I personally believe that most of our products designed for end users work this way. Even many people I've talked to working on advertising see a large part of their job as improving the advertising experience rather than just revenue.
Within search at least, the issue of customer service is scale. It's a challenging problem with millions of users. We do a good bit already, through feedback forms, staffed U2U groups, video questions and answers, and other venues. We recognize that not everyone can share information on a forum either, and so some of these feedback forms are private.
Gmail does the same, although I'm less familiar with their support offerings. A good starting point might be http://mail.google.com/support/. I'd imagine Google+ will grow in terms of it's forms of feedback and support, and the team seems to be quite responsive on a number of issues already. http://www.google.com/support/+/ might also be a good starting point there.
I'm not familiar enough to comment on the original issue, but I would guess that this has more to do with law in the US, specifically COPPA, the Children's Online Privacy Protection Act. IANAL.
Customer service per dollar spent is lower than anywhere else on earth.
(in case you are not)
Yes Google sells user to their paying customers -- advertisers. How do you think they make all those billions of dollars / year? Why are they providing you with free Gmail, Maps, and high quality search results? The answer is that they sell you to their customers. If you are in gmail and sent your mom an email telling her what kind of printer cartridges to buy, don't be surprised if you see an ad about printer cartridges. They indirectly sold your data "interested in printer cartridges" to their "real" customer -- the company that makes printer cartridges and is looking for someone to buy them.
It was a clever comment but it's an oversimplification.