You're right. In the interests of brevity, I omitted some qualifications.
The actual law is:

Penal Code 46.02 (Effective Sept 1, 2007). UNLAWFUL CARRYING WEAPONS. (a)
A person commits an offense if the person intentionally, knowingly, or
recklessly carries on or about his or her person a handgun, illegal knife,
or club if the person is not:
(1) on the person's own premises or premises under the person's control;
or
(2) inside of or directly en route to a motor vehicle that is owned by
the person or under the person's control.
(a-1) A person commits an offense if the person intentionally, knowingly,
or recklessly carries on or about his or her person a handgun in a motor
vehicle that is owned by the person or under the person's control at any
time in which:
(1) the handgun is in plain view; or
(2) the person is:
(A) engaged in criminal activity, other than a Class C misdemeanor that
is a violation of a law or ordinance regulating traffic;
(B) prohibited by law from possessing a firearm;
or
(C) a member of a criminal street gang, as defined by Section 71.01.

Decoding this typical legislature-speak goes as follows:

It is NOT an offense to carry a handgun if you a a) Inside your car, AND
b) The weapon is not visible, AND c) you are not a criminal, AND d) you are
not prohibited from owning a gun, AND e) you are not a member of a gang. If
any of the following is true, you have committed an offense:
1. You're not in the car
2. The weapon is in plain sight.
3. You are a criminal.
4. You are prohibited from owning a gun.
5. You are a member of a gang.

Note that the crate of anvils we call our legislature says you must be
"inside of or directly en route to a vehicle..." Plain reading says you can
take a gun TO your car, but you're vulnerable to arrest if you take the gun
FROM your car.

Go figure.


You decoded wrong. You still must have a CCW to carry a handgun in a
car. http://www.texas-on-line.com/gun.html

" Vehicle carry and transportation: unlicensed individuals and
non-residents may not carry handguns on or about their persons while
in a vehicle loaded rifles and shotguns may be carried in plain view
or in a case "