Greetings. I have a MBP 17" Mid 2010, bought it second hand so no System DVD was included, and recently had the same problem. I spent a couple of days going through all the various suggestions found online. Here's how I solved the issue, hopefully it can still help other users.
- I downloaded a retail Snow Leopard 10.6.3 dmg (installer version 23.1.1, check installer Info if you have doubts) - and yes, I think it was ok for me to download it since my notebook was originally supplied with that OS,
- created a bootable USB stick with it (guides about how-to are common so I won't waste your time repeating the procedure here),
- connected an external hd and erased the content while still on Sierra,
- replaced the internal hd with the new empty one,
- booted from the USB stick,
- initialized the hard drive again, just to make sure, using Disk Utility included in the SL installation,
- launched the installer.
All went smooth and after some 10 mins the new/old OS was successfully installed. I'm now using Snow Leopard 10.6.3 to write this reply.
Things were easier than I thought while reading many forums. I guess a lot of people just throw in their answers without direct knowledge (and this actually makes everything quite annoying and only rarely really helpful so, guys, think twice before you answer: either you DO KNOW what you're saying OR you're complicating things / just wasting your and other people's time).
Note: while I was on Sierra, the SL installer's icon appeared with the typical sign indicating that it wouldn't work. But it did.