The thought process here is that in order to recover from an injury of any type, where the muscle fibres have been torn (as in a grade 1 hamstring tear), you want the various white blood cells to get to the tear site, in order to facilitate healing. In order for the WBC to get to the site, there has to be some sort of imflammation there. Anti-inflams would stop / reduce this.
However, my thoughts are that non-prescription anti-inflams are not going to be strong enough to sufficiently reduce swelling so as to stop the above process. In my experience of hamstring pulls, the best time for anti-inflams is directly after training/rehab to prevent soreness which might appear afterwards. Also, try tiger balm in future (I imagine your hamstring is well healed by now!) on any pulls when you start training - its a life saver.