I think they turned to LFS for the second most popular reason: They looked around and didn't find an existing distro that met their needs. (I'm assuming the most popular reason is to really learn linux.)
As someone else pointed out, they (Luis and Mike) wanted a very minimal distribution and it is easier to build one with LFS than try to strip down a full distro. Another reason for using a minimal distro, and this wasn't mentioned in the article, is that the PCs can be loaded by PXE boot. Each library branch has a server, so if they add a PC installation is as simple as plugging it in and turning it on.
Also not mentioned in the article: They modified Mozilla to remove a lot of its menu items and functionality to limit it to what they felt appropriate for a public terminal. For example, you can save downloads only to the floppy drive. This prevents users from cluttering up the hard drive and also makes it easy to protect their privacy: Shut down Mozilla, and everything is cleared. The system restarts it after a couple seconds.
They wanted to build a system that would provide library patrons with the functionality they had under Windows, but which even a malicious user would not be able to damage.
And the reason I have this information is that Luis and Mike spoke at a meeting of the Columbia Area Linux User Group (calug.com).