Fork width change was for larger tyres,
BSA used the triumph hub from 68 on (least for the TLS braked bikes)
Larger (3.50 vs. 3.25) front tyre was fitted to T120TT, TR6C and T100C from '67, Triumph fork legs were 6-1/2" centres 'til '69.
Complete Triumph 8" TLS and 7" SLS hubs/brakes were used on BSA's from '68 (the 7" SLS certainly on the new-for-'68 B25 and C25). Both hubs used the W1641 spindle, from the Triumph 6-1/2" centres forks; however BSA fork legs were 6-3/4" centres, which necessitated '68 one-year-only sliders.
More likely Triumph forks were increased to 6-3/4" centres for fewer one-off slider parts?