My BLO-finished stocks do not get sticky in hot weather. Whomever applied the oil to your friend's stock either applied it too thickly or didn't wait long enough between coats. Straight BLO is a beautiful and classic finish but it takes A LOT of patience to apply if starting with bare wood. I think the saying goes one coat a day for a week, one coat a week for a month, one coat a month for a year and then one coat a year to maintain (maybe a slight exaggeration but not too far off) and any spots that still look wet an hour after application should be wiped. It needs to dry in the wood and not so much on the surface. And you buy it 'boiled' as opposed to raw (although as Boom Boom said they don't actually boil it anymore). Tru-Oil is just linseed oil with extra additives to speed up drying. It does tend to come out glossier than I like because it will dry on the surface, but it's definitely faster with less risk of staying sticky. Lin-Speed is a similar product from Brownell's.
For the OPs rifle, it's pretty safe to clean the stock and rub on a light coat of linseed oil with your fingers and see if you like the result. I've done that to several myself, just use a little at a time. Like barely enough to spread around. Some worn areas will soak up the oil more quickly, and you can redistrubute the oil from other areas of the stock to those dry looking areas after setting a few minutes but resist the urge to keep adding more. then give it a a few days to dry. May only take 2-3 applications, maybe more but the key is thin coats and enough drying time between them.