STORY UPDATED: check for updates below.
Does the forward assist on an AR-15 switch the firearm from "regular semi-auto to overlapping-auto"? No, that's not true: The forward assist is used to manually close the bolt of the AR-15 and has nothing to do with the AR-15 being a semi-automatic firearm. Additionally, the post in which the claim appeared is clearly satire.
The claim appeared in a Facebook post on July 8, 2022. It has a screenshot of this tweet, which has a picture that identified a forward assist on an AR-15. The screenshotted tweet reads:
I am prior service armored infantry for the Coast Guard--for those unfamiliar, this is the button that switches your AR from regular semi-auto to overlapping-auto
A civilian has no business with this capability.
This is what the post looked like on Facebook at the time of writing:
(Source: Facebook screenshot taken on Tue Jul 12 20:15:08 2022 UTC)
The Facebook page where the post was published is identified as a satire page where "nothing posted is considered true," as shown in the screenshot below:
(Source: Facebook screenshot taken on Tue Jul 12 16:54:21 2022 UTC)
The tweet that originally made the claim was a satirical joke. In several tweets that followed the original -- including those found here, here and here -- the Twitter account that originally posted the claim implied that the original claim was sarcasm in response to tweets critical of civilian use of AR-15s (here and here).
The forward assist is used to manually ensure that the bolt of the AR-15 -- which is a part of the bolt carrier group of the firearm that is responsible for loading and sealing the chamber for firing -- is closed. It is usually only used if the bolt won't close on its own, which may occur if the firearm or ammunition is dirty. The closure was originally developed for military use and doesn't have anything to do with an AR-15 rifle being a semi-automatic firearm.
Lead Stories also didn't find any evidence of an "armored infantry for the Coast Guard," as mentioned in the post that originally tweeted the claim.
There are articles (here and here) and videos (here and here) explaining the purpose of the AR-15 forward assist. None of them mention that the forward assist changes the firearm from a regular semi-automatic firearm to "overlapping-auto."
Updates:
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2022-07-18T22:47:59Z 2022-07-18T22:47:59Z Added more clarification that Lead Stories recognizes that the claim is a joke. Added statement about the "armored infantry for the Coast Guard" claim from the original tweet.