They are correct... changing this setting would allow your timeout to be extended... it would allow you to do things like send emails to thousands of people over hours or even days. This is actually what you want to do. If this hosting provider won't let you, then they won't let you...
You could either update the account with them so that they would let you, or use another hosting provider that doesn't have that restriction. Who is your hosting provider? Many large hosts don't have that restriction even on their basic accounts.