Well the way you describe it sounds to me like developers are rather trying to help you get them more productive.
In my experience, the border between developer and external testing is quite fuzzy and flexible and much depends on a concrete project details. I for one have been working in projects with dev:tester ratio varying from 10:1 to 1:2 and all of them went well and fine. The only one that sucked was where there were no testers at all - and it sucked really bad. :)
That border I mention above gets even fuzzier if you take into account that there might (maybe even should) be close collaboration between developers and testers. Eg, developers might contribute quite a lot into product testability while testers contributing into getting specs and design right at the early stages.
It's hard to tell beforehand what amount of testing would be most productive to "offload" to external party in your case, but your note about ...testing the code against the specs, eg. when you click on 'submit' the index page should load... makes me feel like your team can gain some significant performance boost if you wisely hire one or two professional testers or QA consultants. If you get these guys right, you'll not only get immediate gain but also will get someone to help you tune the right dev:testers balance in your team.
- By the way, before diving deeper into these tricky matters I would recommend you to do some preliminary study. For that, you can eg simply study job descriptions in vacancies from successful software companies (there's plenty available in the web). Find out which are core competencies considered for testers and which are ones typically expected from developers, try to "sense" the differences and similarities. This study may help you make more informed decisions further down the road.
PS. developers are rather trying to help you get them more productive -- for the sake of completeness have to note their argumentation does not look very compelling. The bias they refer to is a real and serious issue but I think it can also be addressed without involving third party - eg by making them cross-test each other. In my experience this trick helped to tame bias to tolerable levels (though have to admit it pales in comparison to "surgical" objective analysis done by qualified professional tester). I believe that most critical issues solved by employing third party testers are more related to matters of professional focus and productivity, division of labour... stuff like that.