I totally agree. I see small-time operations all the time using free e-mail services. I feel embarrassed for them.
I also saw a company that was asking people to register for something. To register, you had to fill out a form. The thing is, the form was a PDF hosted on a free Dropbox account in the account's public area. To make matters worse, it wasn't even a PDF form where you could type in it. You had to print it out, fill it out by hand, then scan and e-mail it back or fax it. Yikes!
Also, the last place I worked did business with a local data storage company for tape and paper archiving. When you had a box ready for them to pick up, you went on their website and filled out a web form. That was alright, if a little barebones looking. But when you completed the form, you had to press an "Email" button to notify them of the box number(s) and date that it needed to be picked up. The thing is, instead of it just notifying them via some backend system, it opened a compose e-mail window in your default e-mail application with their e-mail address as the recipient and a subject containing the company and box codes and the date for pickup. That really surprised me. They couldn't have scripted something through sendmail/exim/postfix on the webserver itself?
Sometimes it's the little things that give you away.
Back on topic, I'd agree that if the site has business purposes of any kind that .com is the way to go. But if it's just a site about and others to learn about you, that's what .me is for.
