"many eyes make all bugs shallow" is logically correct. No it is not. Bugs are usually found after they manifest themselves. Then the bug is searched for. Before that, it happens extremely rarely that a bug gets found in the source code.
It is a statistically higher probability that a bug *has the potential* to be identified quicker and/or fixed quicker with FOSS than with closed source. If that would be the case, we would hear regularly about such bug fixes :D
Btw, "professionals"? Are you serious? You seriously think that FOSS developers are inferior in their competency compared to a developer who works at a company? I mentioned "hobbyists" did, I not? Of course there are plenty of professional developers in the FOSS area. But there are also plenty of very bad developers.
E.g. look at the source code of lucene: http://lucene.apache.org/ half of it is completely unmaintainable.
Before opening your mouth so wide you should perhaps stop simply "using" FOSS but look into the sourcecode or debug it.
I saw plenty of "bad code" form professionals ... however I saw no real prime example of good code in FOSS.
The reason why many OSS is _good_ and has relatively low bugs is because a small core team of _professionals_ is crafting it. Not because it is FOSS or because many eyes are looking on it.