If it’s a Linux server, the operating system is what it is and has always been case sensitive, you just haven’t encountered a problem with it till now.
Given the information you’ve provided, I’d probably side with the web host. “Low-cost web hosts” (probably shared hosting) usually give you basic and limited control over a Linux web server. It’s generally up to the user to determine whether that will give them sufficient control over the hosting environment and whether they have the server administration knowledge required to fix or reconfigure things to suit their needs.
Most basic hosting I’ve used gives you access to some administrative tools (control panel) that can help you resolve something like this on your own.
There have been some previous ConcreteCMS forum discussions on case sensitivity. If you want to resolve the problem using ConcreteCMS, perhaps it will give you some additional hints on how it may be done.