The yeshiva I graduated from (a well known, respected, chareidi yeshiva) plays the national anthem at graduations. The Rosh Yeshiva said that we live in the USA, and we need to show hakaras hatov to them.
I think it definitely should have been played at the siyum.
If they would have sang the National Anthem, then some people would have expected the Israeli NA.
Both of these. I think they did the right thing.