The code in v0.5.12 should not create those small outputs - it should get added to the fee.
I think the user might have used an earlier version of MultiBit without realising.
If you look at the tx at
https://blockchain.info/tx/5ed5a26683ad83d0fed3938d8424c2568da7ca0490edb47029acaf82e8d2afd4 the size is 1117 bytes but it only has a fee of 0.0001 BTC. The 0.5.12 code would set the fee as 0.0002 BTC for a tx of this size.
Can you double check with the user that the value in the "About MultiBit" screen of the MultiBit that they used to create the tx is 0.5.12 please ? Also, if the user clicks on a bitcoin URI on a webpage it can open an earlier version of MultiBit (it depends on what they have registered as the URI handler) so if you could check if the user did that too that would be useful.
In another instance of there being a tx with small change it did go through eventually (after several hours).
Edit: Also, the fee that they have set - 0.0001 BTC - is small for that size of tx. It's below the minimum relay fee of 0.0001 BTC / KB of tx. The user has changed the default fee value set (in versions earlier than 0.5.12) from 0.0005 BTC to 0.0001 BTC. This can increase confirmation times for regular tx when you send them.
