Does the destination country’s historical relationship to the country of origin matter (for example, france used to colonize syria, iraqi's may be fleeing a war the us was intrinsically involved with, etc).

To some extent it does.

Many of the old colonial powers such as Britain, France, Belgium, Spain etc have sought to enforce a modern 'sphere of influence' through cultural exchange programs, immigration, trade, education etc.

For these countries, such programs help to maintain a superiority over former colonies and provide socioeconomic advantages.

Hence, if these some countries fall in trouble, these former colonial powers should share the burden.