I guess you're not a programmer, and therefore don't know what a shallow bug is. Conveniently, the rest of the sentence you alluded to explains the term:
"Given enough eyeballs, all bugs are shallow ... the fix will be obvious to someone."
If you have to dig deep into the code to figure out what's causing the problem and how to fix it, that's a deep bug. A bug that doesn't require digging is shallow. Heartbleed was fixed in minutes or hours after the symptom was noticed - a very shallow bug indeed. "The fix will be obvious to someone."
The presence or absence of bugs is an orthogonal question. That's closely correlated with the code review and testing process - how many people have to examine and sign off on the code before it's committed, and if there is a full suite of automated unit tests.
The proprietary code I write is only seen by me. Some GPL code I write also doesn't get proper peer review, but most of it is reviewed by at least three people, and often several others look at it and comment. For Moodle, for example, I post code I'm happy with. I post it with unit tests which test the possible inputs and verify that each function does its job. Then anyone interested in the topic looks at my code and comments, typically 2-4 people. I post revisions and after no-one has any complaints it enters official peer review. At that stage, a designated programmer familiar with that section of the code examines it, suggests changes, and eventually signs off on it when we're both satisfied that it's correct. Then it goes to the tester. After that, the integration team. Moodle doesn't get very many new bugs because of this quality control process. That's independent of how easily bugs are fixed, how shallow they are, depending on how many people are trying to fix the bug.