As stated before, BSM is an acronym for Better Sprint Mod, a client side modification that allows a user to keybind sprint to a particular key and forces the user to continue sprinting whenever the client detects that the player has stopped sprinting. Though the use of this modification is fairly common, its use on MCGamer's network is strictly prohibited as it's been proven to provide an unfair advantage to players who have it installed against players who do not.
Accusations of Better Sprint Mod are fairly common simply due to the abundance of players who have it installed without realizing it's against the rules. However, many players also accuse other players of hacking or cheating simply due to the fact that the other person's killed them and they're frustrated. I wouldn't take this isolated situation too seriously: you're aware that you don't have the modification installed and unless the user has some solid codemning proof no action will be taken against you.
Where accusations become a problem is when a user continues to follow you into games harassing you and continually accusing you of using illegal modifications or clients. Should this happen, take a screenshot by either using screenshot software, Minecraft's built-in screenshot system (by default this system is keybound to F2 and the images are saved in your .minecraft folder under screenshots), or by simply print screening your entire screen and saving the image. As with all screenshot-related proof, ensure that the image is unedited and uncropped. It's suggested that with cases regarding harassment that you take multiple screenshots and have some indication that you've told the user to stop harassing you to further strengthen your case.
When you've gathered sufficient evidence, you may submit a Report Abuse on our forums or even contact a Moderator directly on our TeamSpeak to have the user dealt with.
Accusations are unfortunately a part of the game in a large community, but so long as you know you're not hacking or cheating there should be no reason that you should feel threatened or uncomfortable by another user.
With that being said, continue to enjoy your time at MCGamer and MCSG. I look forward to your contributions to this community and I hope to see you around!
This thread has been sufficiently answered, so I'll be locking this thread. Feel free to post another thread or personal message myself or another staff member should you ever have any comments, questions or concerns! :]