Instagrid is another webapp that let's you access your Instagram photos on the web. I think because you log into Instagrid, users who know your Instagrid URL can see all of your photos, whether or not your account it set to private. Instagrid doesn't have a directory listing, so I think the only people who can access your feed is those you give the URL to. So, even if my account was set to private, you would (and can) see all of my photos there - for example: http://instagrid.me/jaredharley/.
From Instagram's FAQ:
Who can see my photos?
All photos are public by default which means they are visible to anyone using Instagram or on the instagr.am website. If you choose to make your account private, then only people who follow you on Instagram will be able to see your photos.
I think being able to see an Instagram user's photos through another website is a limitation of the Instagram API - the webapp has no idea if someone has their account set to private or not. If it was, you'd have to have the possible viewer log in to Instagram at the webapp, then check and see whether the user is allowed to see your Instagram feed.
In either case, Instagrid does give you the ability to view the images full-sized and download them.