Not entirely. The point of the article is that, big VCs have strong name recognition, and should they invest in you in the seed stage, they can refuse to give you further funding and no other VC will step in to help you because they will wonder why your initial investor, who knows you best, didn't step in and keep investing. So the big VC has de facto monopoly "dips" in your company.
That suggests there is some kind of optimal path in which financing to choose from what supplier at a certain stage, but I think that to be associated with a large VC usually should compensate for the downsides during a follow up round.
Simply approach another VC after getting financing from the 'first big one', and make sure that you are allowed to do so.
VCs love to be #2... getting them to be #1 is the hard part.