It really depends on the company. Companies like Google and Facebook are very unlikely to hire people at a higher level than their previous level (though certainly it happens). That's easier at smaller companies.
People say this, but I think they mean that you can go from L3 to L4, or L4 to L5. It is very difficult to come in at L6, and it's even relatively hard to come in at L5, where L3 is new college grad.
Also, if you come back within a certain timeframe, you don't have to re-interview, but you also don't get a bump in level. That timeframe is usually a year or so. I'm not sure if they would even allow you to re-interview if you come back within a year, but I'm not sure of that part.
I should also say that I see this claim a lot, but I am on a hiring committee and I have never seen this happen. I'm sure there are some people for which this works, but I think it's more rare than people know. I also suspect that the vast majority of people are leaving at L3, and coming back at L4. If you are good at doing a Google interview and have some experience, it's not that hard to interview at L4 and get in.
Now what I have seen is someone leaving for two or three years and coming back in at a higher level. But that seems like it is based on the experience they gained outside of Google, not that they were necessarily passed over for promotion while at Google.
Now the promo process at Google is the absolutely worst process for promotion I have ever had to endure, so I'm positive that good engineers are passed over on a regular basis. But this idea you leave and come back in a year to get your promo is more myth than reality.
So I’ve def seen someone come back from uber L5->L6 but it’s probably rare (but then L6 itself is relatively rare) and under a year. And I’ve been told by VP that it does happen (I was doubtful too) but needs director? approval. Heard of may cases below L6 though