Not specializations. I was discussing the Ranged(Heavy) skill, which can be increased to 2 during Career/Specializaion (sometimes referred to as Profession in the book) .

It doesn't matter which tree it's from it's still the same Specialization and you can't take the same Specialization twice.

I think it was one from the Bounty Hunter Career, and one from the Assassin Specialization. That would work.

The ruling I'm referring to is on page 35 under Select Specializations

"During this step of character creation, the player may choose two of the four additional career skills and gain one rank in each (without spending experience). He may not choose the same skill more than once. However, he may choose to train a skill that was also trained during the career selection step, allowing the character to start with a skill trained to level two."

Looks right, my mistake.

As long as the player is aware of and fine with the fact that their Hitman won't be much use to the party outside of Hitmanning things, and they agree not to complain when the party decides to resort to methods other than Hitmanning when solving problems, then I see no issue with overly investing in one area.

Of course it also doesn't hurt to occasionally throw them an OCP to remind them that they aren't awesome at everything, like a Melee-specced Marauder who ambushes the Assassin up close...