He might be getting some high-school chemistry/physics a little confused.
Forget about "air" for the moment, and think about individual gases (eg, oxygen, nitrogen). In their normal, room temperature states, these basic chemical elements exist as a gas.
You have probably heard of liquid nitrogen, often used by chemistry teachers to dip stuff like fruit into, and then hit it with a hammer and watch it shatter. Like any other element, when a gas is cooled, it will turn into a liquid. Cool it even further, and it will turn into solid matter. These state-changing temperatures vary hugely between different chemical elements.
Where your brother-in-law may be getting confused, is that the temperature at which a gas will condense into a liquid is effected by ambient pressure. For example, water is a solid (ice) at 0C, or 32 F. It is a gas (steam) at 100C, or 212F. But only at 1atm. If you increase or decrease the pressure, you will adjust the freezing and boiling points of a substance.
Having said all that, and probably making buggerall sense in the process, air in a SCUBA tank is not compressed enough to be able to change its state at normal operating temperature.
Either that, or he's been watching The Abyss too much...