In looking at this statement we have to first do one thing, separate liberalism in two forms, classical liberalism and modern liberalism. As these are very different from another they cannot be grouped together for this question. Hopefully this will let this question be answered more easily and perhaps an answer can be made for it. For classical liberalism a case can certainly be made for a fear of unchecked power being at its heart.
Early classical liberal political commentators and philosophers based their beliefs on one simple overriding one – the state is a negative influence on people's lives and they wished to be from its persecution of them. Classical liberals are advocates of 'negative freedom', freedom from external restraint. Whilst this applies to many things other than a fear of an over-powerful government this stemmed from the liberal philosophers Locke's view on democracy.
Locke believed in government by consent. The propertied should be able to elect politicians to protect themselves from the government and in particular taxation. Locke believed this would check the power of government as the propertied could then defend their natural rights against government. Government would then operate as a representative assembly. Other early liberals belied democracy could become dangerous, they saw the possibility of democracy becoming the enemy of individual liberty.
They saw democracy as applying majority rule and forcing the will of the majority on all individuals if they wanted it or not, liberals believed minority rights and individual liberty would be crushed in the name of the people. Nineteenth century liberals saw democracy as the Ancient Greek philosophers Plato and Aristotle did, a system of rule by the masses at the expense of wisdom and property. All of this gives this appearance of a fear of unchecked power being at the heart of classical liberalism, a fear that democracy if given too much free reign could crush the rights of individuals.
Other classical liberal arguments including those for social darwinism and beliefs on social equality support this. Classical liberals believe so firmly in laissez-faire economics and that humans were self-reliant that the state should not attempt to look after the few who were too weak to look after themselves. They believed giving even this much power to the state would be detrimental to their lives, as it would take their money in tax to look after these people who they believed deserved what they had in life as they had earned it.
It is easy to conclude that at the heart of classical liberalism certainly lies a fear of unchecked power and that classical liberalism as an ideology is about combating that power and making certain it can not have any influence of individual rights and freedoms. This fear of unchecked power is overriding and influences all classical liberal ideas. In modern liberalism it is more difficult to find a fear of unchecked power. Modern liberalism does not seem to share many of the same values with liberalism.
It still believes people are born with unequal merits, that some will rise and others will fall however modern liberals having seen the new forms of injustice caused by the industrial and capitalist revolutions advocate looking after those that fall with a 'safety net' state. This power given to the state would never happen in a classical liberal system but that does not mean that the classical liberal fear of unchecked power has been removed. Modern liberals were not believes in 'negative freedom' but in 'positive freedom', individuals are free to develop and attain individuality.
Modern liberals look at negative freedom and would see that the removal of external constraints may amount to no more than the freedom to starve and the freedom to die, while positive freedom aspires to empower the individual and safeguard people from social evils that could cripple their lives. Modern liberalism does offer freedom from, but as seen in the Beveridge Report of 1942 and the Atlantic Charter of 1941 these were freedoms from want, fear, ignorance and disease rather than the classical liberal freedom from external restraint.
Modern liberals share the preference, with classical liberals, of self-reliant individuals who can and do take responsibility for their own lives, but believe in one essential difference, that this is only possible if social conditions make it possible. Modern liberals firmly believe in the importance of the individual before that of society or of the state but understand that equality of opportunity must be given for all to succeed as some are born with far more opportunity than others and some are born with little or no opportunity at all even if they are a brilliant person.
Classical liberals would not believe in this and would see any form of helping individuals as the state overstepping what its boundaries should be and that people can make it to the maximum of their ability without help from the outside. At the heart of modern liberalism would seem to be a belief that the state should help individuals help themselves to become the best they can and give equal opportunity to all rather than help no one for fear of the state becoming all powerful. Modern liberals do fear unchecked power but not to the overriding extent that classical liberals do.