Are we sure this Rudy's isn't actually in League City?
I'm positive. Of course, anyone who was really picky and not interested in taking a unknown's word for it could go look it up on the City of Webster's online map of registered plats:
http://www1.cityofwebster.com/ArcGISonline/Web/Plats/index.html
They'd end up finding the current plat, (.pdf warning)
http://www1.cityofwebster.com/link/PlatProject/133.pdf, where the Rudy's in question is in section "B1".
Also, here's Tesla's EAB file record with the TX Dept. of Licensing and Regulations for the Supercharger build at that site, which shows Webster as the city:
https://www.tdlr.texas.gov/ABDataSearch/SearchResultDetail.asp?1=EABPRJB8811383
Project Name: Tesla - Tx035
Project Address: 21361 Gulf Frwy
City: Webster Zip: 77598 County: Harris
Scope of Work: Installation of 10 electric vehicle charging stalls, 5 equipment cabinets, 1 switchgear, 1 utility transformer
Building/Facility Name: Rudy's Bbq
Or, if all that's not good enough for you, when I called the City of Webster's building department last week after I stumbled across the TDLR filing as part of my own "Future Supercharger Sites" sleuthing to ask whether a building permit had been pulled yet, they told me, "Yes." Sort of. The gist of the information I was given was that the permit has been sitting in the building office for some weeks/months now but they haven't been able to get anyone to come pick it up. They've called Tesla (or whomever their point of contact was for the application) a number of times but can't seem to get ahold of anyone or get called back.
At least that was what I think was being said. I hope this is just a combination of Tesla's seemingly usual "we move fast and therefore easily get disorganized" and their temporary (hopefully?) slowdown of the SC build out during 2018 Q3/Q4 as they push for being cashflow positive and/or profitability. Frankly, IMO, this particular site isn't that important. Now that Ft. Stockton and Pecos are in, I would prefer them to work towards getting SCs installed in Lubbock, Wichita Falls, and Ft. Smith (Arkansas) long before they put serious effort into this site.