Average Software: I was assuming a lack of modifications to be implicit in "so long as you're including the whole framework".
Whether you modified SDL or not is irrelevant. If you ship it in binary form, you are now a distributor and the conveyance clause of the LGPL (which is inherited from the full GPL) comes into effect. At this point you must provide the source in a GPL accepted manner.
The line I use in my README to satisfy the LGPL license requirements is:
I consider this to be sufficient both for providing the original source and also the text of the LGPL, since both are available at that link.
If I'm doing this wrong somebody tell me quick.
That is wrong. You must include a copy of the full license.
As for the source, it depends on whether SDL is licensed LGPL2 or 3, which I'm having trouble determining from their website (they say 2 but link to 3).
Your notice is not sufficient for LGPL2, you must bundle the source.
I believe the notice would be sufficient for LGPL3 if you changed the link to reference the exact source code used by the binary you distributed. However, you're liable for that source for what seems to be a term of 3 years, so if the address you provide changes, you are no longer in compliance.
Note that SDL website says this:
If you include the SDL library in binary form, you should also make available the source code to the version you provide
Your safest bet is to ship the source.
Disclaimer: I am not a lawyer, but I've researched this stuff pretty extensively for my own use. I've never used SDL, so I never looked too hard into this particular case.