If the BoS has it then it's not technology going unchecked

Neither is the technology that the institute has.

Using technology to murder innocent people isn't really what I would call checked.

If you're using it to knowingly kill people, then its checked. If it is killing people without your knowing, it is unchecked.

To keep something in check means to keep something correct, what they are doing it not morally correct, which is the subject since it's what the BoS are trying to achieve, moral correctness.

Usually, keeping something in-check means to keep it out of civilian hands. If something is unchecked, then EVERYONE can get at it.

Anyways, morals in the Fallout universe don't work the same as they do here. To them, they are morally correct in using any lethal force necessary to keep dangerous technology out of the hands of non-Brotherhood. To them, they are keeping it in-check and will use the technology sparingly, like with Liberty Prime. I haven't played Fallout 4 yet, so I don't know their deal there.

Mmm, no keeping something in check means to keep in control, it's morally uncontrolled top murder innocents with technology, that doesn't have anything to do with civilians, and The Institute are certainly not civilians, not even in the eyes of the BoS.

Their reasoning is that it's morally wrong for the institute to use technology in that manner. Of course, but the BoS perspective of morals is the only perspective that matters here, since we're discussing the BoS view on the dangers of technology.