A washing machine consumes about 100Wh == 360kJ for a load (ref: http://www.rpc.com.au/information/faq/power-consumption/wash...).
The Emma Mearsk, one of the largest container ships around, uses 13 tonnes of fuel an hour to transport 18000 containers, over a distance of (say) 20000 kilometres, which is 1kg of fuel to transport one container 45km (according to Wikipedia: https://en.wikipedia.org/wiki/Energy_efficiency_in_transport...), or 450kg for the whole distance.
A 7.5kg washing machine load occupies about 0.00025 of a container, so the fuel requirement to transport that washing machine load is 0.1kg.
The ship's engines use 0.163kg of fuel to generate one kWh, so the energy consumption for just the transport of our washing machine load is 0.6kWh, or 2200kJ.
360kJ of USA residential electricity will cost about $0.015. (Pulled randomly from: http://www.eia.gov/electricity/monthly/epm_table_grapher.cfm...)
0.16kg of heavy fuel oil in Singapore will cost $0.05. (From: http://shipandbunker.com/prices/apac/sea/sg-sin-singapore#IF...)
This is, of course, horribly simplified --- e.g. I'm not calculating the cost of washing water, or transport from the container port to the owner's house --- it does at least show that big ship shipping is really, really cheap. While I still think the original author is wrong, they are at least plausibly wrong.