A family of Microsoft relational database management systems designed for ease of use.
I don't see how that code block could cause your issue. All it's doing is setting the Visible property of several controls, and that "setting" has been around for all versions of Access.
Are you sure your references are set correctly for the older versions of the runtime?
I had a similar situation where I was referring to a constant that was not available in 2002/2003, but had been introduced in 2007 or 2010. The code compiled fine, and it would run okay until it hit that constant on a machine running 2002 or 2003. Once it did, I received an error (can't remember exactly what error it was, but it was similar to what you're getting).
So be sure that you're not using any features or constants that are NOT available in 2002/2003.