Yes, that is true. This is why American liberalism never really got in bed with Marxism, a few traitors notwithstanding. That explains the motivation. That does not explain the policy. Indeed, Western governments are not driven by barbra-streisand airheads; these are well educated, capable of logical thought, with access to every technological resource people. If not themselves, then their advisers would tell them that putting hundreds of thousands of people without skills or property, that belong to different and hostile religion and culture, would disproportionately hurt not the ruling class but the indigenous working class. Why do they do it to their own, -- German, Dutch, British poor?
Further, there is no need to be all that liberal politically to be compassionate to the refugees. Christian leaders, including conservative ones, call for charity too -- it is their job. At issue here is not humanitarianism but a destructive policy aimed at the national working class.
I still think that at work here is an active desire to destroy the Western civilization. It is not just do-goodism. The natural sentiments of compassion, that resonate especially well with the liberals, but are not unique to them, are how the enemy of our civilization sells these policies to the masses in the developed countries. The natural sentiments of envy and desire for equality and justice is how the enemy of the Western civilization sold Marxism to the masses a century ago. The sentiments differ, the end result is the same: erasure of national identities, destruction or rational economy, submission of religion to the state, formation of dictatorial ruling class.