I'm not sure why so many find this so difficult to do. If you are able to place your ship FLAT on the table, it is NOT considered to be an overlap, regardless of whether or not it's in actual contact with the obstacle. The same applies to ships.
If you CANNOT place your ship FLAT on the table because part of it's base is OVER the obstacle, then you have overlapped it.
The term "touching" ONLY applies to ships that have overlapped other ships, as in "ships that are touching cannot attack each other". The same term has never applied to ships and obstacles. You're either on the obstacle because of an overlap, or you're on the table. You can never be FLAT on the table and suffer the effects of an obstacle just because you happen to be in contact with it.
It most certainly is an overlap. If you make any contact with the asteroid you are overlapping. IF I slide the base - flat on the table now - and it bumps an asteroid but stays flat on the table that is certainly overlapping because no matter how small, if there's contact the rock moves. If you touch a rock you're overlapping pure and simple. If you think otherwise, try sliding your ships around so as not to 'overlap' anything. You said as long as it's flat, no overlap, right? Touching, or contacting, or overlapping (whatever you'd like to call it) an obstacle has always been roll and lose your action - possibly your attack too.