http://www.cowmuffins.net/stuff/___doesntcrash.j2l
http://www.cowmuffins.net/stuff/___doescrash.j2l
You can guess which one is which. The only difference is that the latter one actually uses the second animated tile (exactly five times). So it appears it does require that the tiles actually be used. By the way, instead of doing a full cycle you can trigger the crash with jjk (hence the 1ups).

Note that this level only uses 2 animated tiles. I wasn't able to get it to happen with just 1, but that might have just been my patience (fewer animated tiles/uses means crashes happen less often; I tried about 100 times before giving up). Interestingly, neither the size of the tileset nor TSF vs 1.23 seems to make a difference.