The following quotes are taken from Spirits, Fairies, Leprechauns and Goblins - An Encyclopedia, by Carol Rose (highly recommended).
In the entry for Brownies:
Families were proud of their Brownies as they brought good fortune; to
lose one was disastrous. [...] In general, the Brownie was the most
industrious of the household spirits, ploughing, reaping, grinding
grain, cleaning the house and barns, churning butter - in fact, most
of the tedious jobs he would gladly do. In return the Brownie was
entitled to a bowl of the best cream and new baked cake or bread, to
be put within his reach. To offer the Brownie any form of payment
other than this, especially to take pity and to give him new clothes,
was an insult, and he would vanish immediately.
In the entry for Tomtar:
Tomtar are the Little People in the folklore of Sweden.... They enjoy
a bowl of porridge, and some bread and tobacco, but only on Christmas
morning. To give the Tomtar any better gift during the year would be
sure to offend him, and he would do no more work.
In essence, then, your theory is correct - it is a warning not to spoil your servants. However, I'm not sure that this is because it will "go to their heads". My impression is that brownies, and similar beings, want to work on their own terms. To turn it into a payment, or transaction, was highly insulting to them, particularly if they wanted to do the jobs they want because they enjoyed it, or liked the family. To take pity on them, implying that they are lesser beings relegated to housework, causes offence, and this is the reason they leave - not that their newfound power has gone to their heads. Beings such as Tomtar and Brownies, then, seem to like appreciation, but not payment.
