I read that the actual benefit of flossing your teeth is not to remove food that is between them, but that your gums actually become stronger at fighting infections.
Is this true?
The main benefit from flossing appears to be to reduce gingivitis or gum inflammation. Presumably it does this by removing food from the interdental spaces because there is only weak evidence it removes plaque which might be causing gingivitis. This Cochrane review concludes 
There is some evidence from twelve studies that flossing in addition to toothbrushing reduces gingivitis compared to toothbrushing alone. There is weak, very unreliable evidence from 10 studies that flossing plus toothbrushing may be associated with a small reduction in plaque at 1 and 3 months. No studies reported the effectiveness of flossing plus toothbrushing for preventing dental caries.
 Sambunjak D, Nickerson JW, Poklepovic T, Johnson TM, Imai P, Tugwell P, Worthington HV. Flossing for the management of periodontal diseases and dental caries in adults. Cochrane Database Syst Rev. 2011 Dec 7;(12):CD008829. doi: 10.1002/14651858.CD008829.pub2. Review. PubMed PMID: 22161438.