Sure, but job safety is another issue. The argument in question was that you have a more stable environment in a large company regarding the topics you are working on. In my opinion, this isn't the case. Think of the engineers working on Google Wave or discontinued Sun technologies.
The argument was that you would probably work on something "long enough to accomplish something", and that's true. I mean, the Google Wave team did accomplish something. That isn't always true at a startup. Many times, you get hired to work on something that you never complete because you're constantly diverted to go put out fires elsewhere.
I work at one of the national labs. Almost everyone on my floor is an ME (I'm an EE, but I'm writing code). The majority party in this Congress hates what we do (renewable energy) and thus it is extremely likely that a large part of our budget will get cut next fiscal year. So in our case, lots of engineers will get fired when our projects get canceled. Partisan bickering might not get a budget passed before the fiscal year starts (October 1), but I'm saving money and paying off debts, just in case.
Sounds like NASA, constantly in limbo because of political disagreement. What's the public line though on wanting to cut money from renewable energy, one of the targeted for being "more efficient" in funding?
Chances are better that the large company is making a healthy profit though. To be sure, this is not true all the time (look at yahoo). However, I think it's fair to say that in general, your job is more secure at a big company than it will be at a small company.
"Stability" in the quote doesn't refer to job security, but being able to work on a project long enough to accomplish results. The point that projects get canceled or changed all the time in large companies is entirely valid.
For a completely technical-minded person who is responsible only for algorithms, and not keen on customer support and such, might not burn out due to a movement among departments.