Sam Altman wrote a post earlier this week about YC only accepting startups that haven't been through another accelerator. It got a lot of buzz and responses including Imran Ghory showing results with some data. Coincidentally, two of his success examples are Techstars companies. I've spoken with maybe hundreds of companies that have done an accelerator (or were currently in one) and want to also do Techstars. My initial reaction to all of those instances was curiosity around what the founders learned during the initial program, and why/how they want to leverage another program.
Start-Up Chile is a great example of a non-dilutive accelerator that could prime a company to take even more advantage of a top accelerator program. This is especially true for international startups wanting to be in a US-based program.
If the founders are great, the idea is interesting with big potential, and the drive and hustle is in the team, then why not accept them into another accelerator? Why not add those founders into a growing network that can always benefit from more great people? Most importantly, if the mentors and support surrounding that program have deep experience specific to that company, there's even more reason.
If you're coming from another accelerator just be prepared to explain the value you want to get out of a program, beyond raising money and connections. The traction, business model, and tech are what get you those things-- not a stamp of approval from a great accelerator. In fact, this is something commonly missed in interviews by many founders.