I find the possible answers to your specific question fascinating:
If it is true, why do insurance companies do that?
In the US there have been studies that show a correlation between higher credit scores and lower risk to the insurance company (and vice versa). Here are some examples:
Texas Business Review, 2003
Federal Trade Commission, 2007 with the full report here.
Of particular note, the FTC report references (on page 21) an EPIC Actuaries study from 2003 which showed an interesting breakdown of types of claims:
[The study] also showed: (1) no correlation between scores and the size of
liability coverage claims; (2) a weak correlation between scores and the size of collision
coverage claims; and (3) a strong correlation between scores and the size of
comprehensive coverage claims.
Note that "comprehensive" coverage are for claims that are beyond the policy holder's control, such as weather damage, theft, etc. The following possible explanation for this is offered on page 27:
The different
result for comprehensive coverage may be attributable to a correlation between having a
lower score and a higher probability of being a victim of automobile theft, because theft
claims are larger than claims resulting from most other events that this type of insurance
covers.
The FTC report also addresses why the overall correlation between credit score and higher claims exists, with the following (wise) disclaimer on page 3:
Several alternative explanations for the source of the correlation between
credit-based insurance scores and risk have been suggested. At this time,
there is not sufficient evidence to judge which of these explanations, if
any, is correct.
On page 31 the FTC report offers some explanations:
A strong credit history, however, might indicate that a consumer has taken care in
managing his or her financial affairs - avoiding loans that might be difficult to repay,
avoiding high balances on credit cards, making sure that bills are not misplaced and are
paid on time, etc. A consumer who is prudent in financial matters may also be cautious
in other matters related to insurance, such as being more likely to put time, effort, and
money into things like car and home maintenance, cautious driving habits, etc. An
overall inclination to be prudent may lead a consumer both to have a strong credit history
and file fewer insurance claims.
Similarly (also page 31):
Researchers have studied attitudes
toward risk, as well as behavior, in financial settings and driving, as well as a range of
other areas including smoking, occupational choice, and migration.
...
Many of the psychological studies surveyed in that article analyze the
relationship between psychological factors and risk-taking in a single aspect of life. The
authors connect these results between financial behavior and driving from studies on
separate groups of people, and posit the theory that credit-based insurance scoring works
because scores reflect the psychological makeup of the individual in ways that affect
insurance risk.
And also (page 32):
Others have suggested that credit history provides information about a consumer’s
circumstances and those circumstances affect the likelihood or size of claims. One
example is that a driver with a low credit-based insurance score may be in a distressed
financial situation. This may cause stress that makes the consumer a less attentive
driver. Being in a distressed financial situation also might give the driver a greater
incentive to try to obtain payment under an insurance policy. For example, he or she may
be more likely to file a claim for a small amount of damage to an automobile rather than
paying for those expenses out of pocket.
Due to the emotional nature of this topic I feel it's extremely important to reiterate the FTC disclaimer here: "At this time,
there is not sufficient evidence to judge which of these explanations, if
any, is correct."
And also please note that all of these explanations are provided for groups and not individuals.