....Using a conversion kit out of a barrel that has a twist of 1x7, 1x8, 1x9 or 1x12 doesn't put enough spin on the bullet to stabilize it. That is what I have been told and have read on the subject. Not to say that it won't work with a slower twist barrel, just that it won't be as accurate.
You are reading it backwards.
1:7, 1:8, and 1:9 are FASTER twist rates than 1:14.
1:7 means the twist turns 1 complete time in 7" of barrel length. If the twist turns once in 14" it is spinning the bullet half as fast as a 1 in 7 twist.
Generally speaking longer heavier bullets need a faster twist rate. .22 LR shoots 30-40 gr, short round nosed bullets so it needs a slower twist.
When firing a .22 LR in a 1:7 AR15 you are actually over stabilizing the bullet or spinning it faster than it needs to. Also the faster than needed twist rate with a soft lead .22LR bullet can lead to lead fouling.
If you want to find out more about picking the proper twist rate for a given caliber do a Google Search on "Greenhill Formula"