The owner wasn't very worried about it since he flies GPS direct everywhere everytime.
And what heading does he steer when the GPS gives him a new DTK? GPS can't resolve heading.
Your error may have been induced by a turn. HSIs in smaller aircraft are almost always connected to a magentic stabilized gyro. The gyro gives your heading reading, "short term" stability. The remote flux sensor gives your heading reading "long term" correction. Following a turn, it is not uncommon for errors to be induced into directional gyros. It sometimes takes a few minutes for the flux detector to correct the error. Typically, corrections are about 1 degree per minute.
If I saw an difference between the HSI and standby compass, I would immediatly look at my slaving meter and check if the slaving circuits have completed their correction. If they have, the next thing to do is see if the aircraft is configured properly in accordance with POH/AFM or compass placards. Sometimes there is a placard that limits operation of the standby compass with certain equipment running. Windscreen heat is one that has been mentioned, but some less obvious ones may be applicable such as one or two radios in the stack.
After all this, check the correction cards for the HSI and standby compass. It's not impossible to have 10 or 15 degree differences between the two. For instance, on one particular heading, the HSI correction may be +7 whereas the standby compass correction may be -7.