How important is a correct frame size for a Mountainbike? Various frame size calculators on the internet spat out 19" for the size of a hardtail mountainbike frame that suits me. The local bike shop insisted 19" is way too small; he only had 21" sized models. I've never ridden a Mountain Bike in my life and I'm only used to handlebar-saddle drops of up to 20cm and ultra long stems. I've test ridden one and due to my lack of judgement I can only describe it as hopping onto a Harley Davidson Chopper, except that the steering was incredibly sensitive and prone to speed wobbles.

According to my research the difference between 19" and 21" is a ca. 1.5cm gain in toptube length and wheelbase. So after correcting with a shorter steam the net difference is a more volatile steering and a longer wheelbase.

I like a stable road bike on a downhill so I am an enthusiastic endorser of smaller frames coupled with very long stems on road bikes. How does a more volatile steering affect a mountain bike on a trail? Since the handlebar is almost twice as wide as a roadbikes, is speed wobble an actual threat for mountain bikers?
I have ridden MTB for years, an fit between most manufacturers 17" and 19".  

I enjoy tight technical Single track, and get bored quickly with long stretches of trail when time from A to B is solely a measure of physical fitness (hence I am not a road rider). I also tend to stick to short 1-2 hour rides. 

I ride 17" bikes. On the fun stuff, I am more agile and able to really throw the bike around and respond to conditions, at the expense of a bit of power and a slightly cramped cockpit.  On the larger bikes I am more efficient and more comfortable when pacing out on straight roads for long periods of time. 

Think of the difference between sizes like a sports car vs a limo. For a blast around a windy road, take a sports car, for an eight hour drive down the interstate, take the limo. Choose the size that suits the riding you will do most often. 

One question I would ask about the shop and salesman - are they MTBers or road riders. In my experience, roadies a more likely to 'round up', and put you on the bigger bike and MTB'er will 'round down' and put you on the smaller. 

Take the smaller bike for a test ride on the road and see if the cockpit feels cramped. Take the larger bike for a ride and see if you are stretching to make tight turns. Imagine being in a tight turn and being thrown off balance, could you move your weight to correct it. Can you hang you buttocks off the back of the seat and still have bent arms - as needed when going down steep hills.

I hesitate to make a recommendation counter to that of an expert you have visited. Find another bike shop, preferably one that specialises in MTB's and seek a second opinion. 

As far as adjustments, modern MTB 'theory' is shorter stems and wider handle bars for stability rather than long stems.