Based on what I know (I'm a traffic engineer), you are absolutely right–it is discouraged, but not forbidden, to cross a solid white line. Here are some statements from the 2006 Texas Manual on Uniform Traffic Control Devices (TMUTCD) (http://www.txdot.gov/txdot_library/publications/tmutcd.htm):
“Where crossing the lane line markings is discouraged, the lane line markings shall consist of a normal solid white line.” –bottom of page 3B-7
“Where crossing the lane line markings is prohibited, the lane line markings shall consist of two normal solid white lines.” –top of page 3B-12
Note that in TMUTCD language, the word “shall” represents a standard, which is the strongest form of guideline and must be obeyed. The word “should” is weaker, and “may” is even weaker.
For any roads to which the TMUTCD applies, these rules would be correct, and would show that your alleged “violation” was not illegal. And the TMUTCD would apply to any state-maintained road.
Now, here's a caveat: The alleged violation occurred on Lamar Street, which is a city street, not a state-maintained road. The prosecution may claim that the controlling law is the city ordinance, not the Texas Vehicle Code and TMUTCD. Unfortunately, they did not state the statute number on the ticket. (I don't know why they can leave that blank and have the charge stand in court.)
The city ordinance (http://www.amlegal.com/nxt/gateway.dll/Texas/austin/thecodeofthecityofaustintexas?f=templates$fn=default.htm$3.0$vid=amlegal:austin_tx$anc=) adopts teh 1980 edition of the TMUTCD, not the 2006 edition. I don't know what the 1980 edition says about solid white lines. The city ordinance also says that a person may not violate a regulation imposed by a traffic control device (a pavement marking, in your case), whether or not the device's display complies with the 1980 TMUTCD. (The city ordinance is TERRIBLE, in my opinion. First they stick with the 1980 manual, and refuse to stay current with the practice that drivers will see on state-maintained roads. Then they say that they can still cite you for disobeying a traffic control device, even if they failed in their duty to display it properly??)
So, they may claim a couple of things:
1) The 1980 TMUTCD stated that solid white lines could not be crossed. (I don't know if that's true or not, but I doubt it.)
2) The city actually intended to prohibit crossing that line, but just didn't display it properly by making it a double line. (But how could you know that? You can't read their minds!)
Either way, I think they are on weak ground, and you have a good case. The markings at the site really should be in compliance with the newest TMUTCD, especially because it's at an intersection with a state-maintained road.