You need to be very wary of anything written in the non-scientific media about science. The media loves woo and controversy because those are the things that garners readers, and that in turn garners advertising revenue.
By way of analogy, suppose as near-adult in gym class someone said "My gym shoes smell bad. Bad! Awfully bad!" Someone else would inevitably take a sniff. If it was bad, really, really bad, he would say so, while gagging. Someone else would say "That bad? Are you sure? Pass it over." That shoe would have quickly been passed around the locker room if it truly did smell worse than death. (Apologies if you are female; females don't do stupid stuff like this.)
The non-scientific media love scientific articles that smell, particularly those articles that smell extremely bad. The media falls under the compulsion of passing these articles around. Good, solid journalism is sorely lacking nowadays. It's much easier to copy someone else's writing than it is to investigate. It's not plagiarism if the original source receives acknowledgement and a fee. You can typically trace those dubious reports that are all over the internet to a single source.
So what's the source of this 27 million year recurring extinction event figure? It's two men who keep peddling this conjecture every other year or so. Here's the article that caused this imbroglio:
A. Melott and R. Bambach, "Nemesis reconsidered," Monthly Notices of the Royal Astronomical Society: Letters, 407:1 99,102 (2010).
Rather than looking to the non-scientific media, it is much better to look to the scientific community and see how much credence they have given to this conjecture. The answer is essentially none. That article has received a grand total of seven (CrossRef), maybe nine (Web of Science) citations in the four years it has been in print. The vast majority of those are either self citations or citations by other fringe scientists who are pushing their own brand of woo. This hypothesis is viewed rather lightly by the scientific community.
Moral of the story: Don't believe everything you read on the internet.
Let's suppose your conjecture is true. What signs would we see of a prior civilization? If the civilization was sufficiently advanced we would see a depletion of resources. If that prior civilization had advanced to the stage of sending stuff into space, we wouldn't see iron where we see it now. We see iron in very, very old banded iron deposits. We don't see any anomalous iron deposits in what would have been cities millions and millions of years ago.
The same goes for coal and oil. Our first discoveries of oil and coil was stuff easily accessible from the surface. Easy pickings. Those easy pickings would not exist if some prior civilization had advanced to the Elizabethan stage, perhaps even Roman level.
What if some calamity had wiped out humanity 2000 years ago? 10,000 years ago? What would a future civilization see millions of years from now? That's a better question. The answer is not much. That future civilization might well not see anything at all. Archaeologists have found fossil records of our ancestors, but that's because we humans are driven to look for those ancestors. A future civilization might not find any fossil humanoids that exhibited a tripling in brain size in just a few million years.
That of course is assuming that intelligent life arose before humanity. That too is dubious. Evolution shows a more or less steady progression in brain size. Dinosaurs might not have been as dumb as people thought 50 years ago, but they were still pretty dumb. Their brains were reptilian. Science fiction writers love the idea of intelligent dinosaurs. That's a rather non-standard view amongst scientists.