Shops can and will do whatever they want. Time has shown us that aluminum scuba tanks made from alloys other than 6061 explode more often than any other type of scuba tank. Shops have realized that they are safer and put less people at risk by not filling these riskier tanks.
To add to this, if your 6351 alloy tank explodes, and someone sues (there will be a lawsuit...lawsuits abound nowadays), everyone is over a barrel. The shop will be run out of business when the lawyers for the other side find out that other shops refuse to fill these tanks due to perceived risk. You will be in trouble when the family of the shop employee who got killed/hurt and their lawyers read your post in this thread about how you know your tank is safe even though you've read that 6351 alloys tend to be riskier. Everyone loses. Is it worth putting a tank monkey's life in danger? Why would you do that? Aluminum tanks can be had for $150 or less used, in great shape, in a safe alloy. Are you willing to put someone at higher risk of injury to save $150?
I will never fill a 6351 alloy tank. No one can make me. I will never ask anyone else to fill a 6351 alloy tank. In my opinion, they are riskier than 6061 alloy aluminum and steel alloys, and I am not willing to subject myself or others to that higher risk.
Will yours blow up? Are you willing to bet so much on the answer, when there is even a slight probability that you might be wrong? Scuba tanks are different than regulators. If a regulator breaks, it rarely destroys entire rooms, or rips off limbs. The stakes are high in tank explosions, so even a slight increase of probability of explosion scares me and scares me good!
On the other hand, I used to agree with you all, before I decided that diving was expensive, and I needed to man up and buy safer tanks. 6351 alloy aluminum tanks make great lamps, mailboxes, umbrella holders, door stops and bells.