I found this very informative article from the Crown Prince company, an anchovy canner and distributor. Apparently the reason for cold storage has to do with the preservation process and product quality:
Anchovies are a "semi-preserved" product. This means that they are not
sterilized by either cooking or pasteurization. Instead, anchovies are
preserved by a salting process whereby salt is used to control
bacteria which would otherwise render a canned product unusable.
The anchovies remain in the salt until just before canning. Therefore,
suppliers do not pack ahead of order. Our anchovies are not packed
until just prior to shipment.
Because they are "semi-preserved", anchovies will eventually break
down and become mushy. The cans may even puff. This occurs because
there is a non-harmful bacteria that survives in salt. This bacteria
can be inconvenient because when it grows it can eventually form a gas
which will puff the can. We repeat that this is not harmful to humans,
but is most inconvenient.
Heat will hasten the growth of the non-harmful bacteria. Anchovies
should always be stored in a cool place, preferably in the
refrigerator. Their shelf life when refrigerated is about 18 months.
If you do not plan on consuming the anchovies or paste immediately
after purchasing, we recommend storing them in the refrigerator. It is
important to note that puffed anchovy cans are not indicative of a
faulty canning procedure, but rather of improper storage subsequent to
Occasionally, customers complain of a white substance in the can.
Often, salt collects around the edges of the fish. This is harmless,
as it is only salt.