Interesting ... the maintainer for this MAME package for Ubuntu may have hardcoded /etc/mame/ as a search path for ini files, where MAME starts to search for a mame.ini. My MAME executable does not search for mame.ini in /etc/mame, in contrast, and I did not find any hints for that behavior in the source code. It could make sense to have it this way when you do a system-wide installation, as possibly intended here with this PPA.
The problem is that this hardcoded /etc/mame/mame.ini defines that MAME search for the mame.ini file in ~/.mame and some other locations, but not in the current directory. If you want to allow for multiple mame.ini files (e.g. one for the arcade machines, one for the TI machines), you have to either add ".;" (period, semicolon) at the start of the value for inipath in /etc/mame/mame.ini, or you have to explicitly specify the inipath when invoking MAME, as I wrote above (which overrides the hardcoded path).