Well, the Americans are basically serving it to them on a platter, so can you blame the Russians? The US has meddled there for over a century.
If the US did not constantly meddle, there would be no reason for any anti-americanism.
For example, whoever heard of anti-Canadianism or anti-Brazil or even anti-China?
Those countries are large and important, but do not consider themselves by default justified to meddle in the affairs of countries around the world, or at least they wait until their input is sought.
Also, the outcome of the American meddling is usually not beneficial for the county in question, despite fluffy talk about freedom, democracy and human rights.
"By their fruits, ye shall know them... "
Look at the state of Middle East, Central America - classical American meddling grounds.
Russia would be a great deal wiser to solve its problems internally than accept any kind of help from the USA.