Please elaborate on what you mean by 'mistakenly released by Chevron' - what makes you think a mistake was made? I doubt that any entity within the company that had the authority/accesses to processes to effect your separation from the company would mess it up. If this happened in Texas, what you may be describing is basically Texas law that says you have to give someone 8 weeks notice before you can sever them. How that plays out from a practical standpoint is that you are informed that you are to be released on a certain date (say, today), and you are given a 'last date in the office' (which might be today, or sometime next week, etc.). On your last date in the office (or whatever work premises), HR collects your company resources including badge and walks you out the door. They no longer want to see your face. However, the 8 weeks comes into play because you remain on the payroll for 2 months from your release date. So if you were informed you were to be released on June 1, you would stay on the payroll - getting those same paychecks - until on or about August 1. Which is, based on the info you provided, what it sounds like you are experiencing. If your 'real last date' was in August, the Chevron medical you have had should continue until the end of the month (August).
Whenever the Chevron medical terminates, you need to have alternative coverage lined up so you can transition seamlessly. That is what COBRA is there for; Chevron will subsidize 6 month of continued coverage, at which point you are on your own as far as having to take major action (finding a replacement insurer).
My advice: consider the above and see if this sort of explains what you are going through - if it does, you at least have a point of reference to think from. Then regardless, get on the phone to HR (TALK2HR) and pester them. If you have extenuating things to discuss - such as backup for thinking that you were truly mistakenly let go - make sure you have names, dates, etc.; they can't work from just a rambling rant.
Unless I am living under a rock, I don't think there is a company-wide conspiracy to screw you out of your benefits - although these be hard times, in my experience Chevron, and especially the people you will find at TALK2HR, have been fair and totally above board. I will say that I personally have had to get them to explain some things to me more than once, but I have never come away feeling like I got the short end of the stick.
Keep calling - take lots of notes of names, dates, subjects, your specific questions and their answers, and keep at it until you understand what is going on, what your specific timelines/deadlines are, etc. I would tell them I haven't gotten the COBRA package yet; they will put it in the mail that day. You can register for the COBRA stuff online instead of filling out the paperwork and mailing it; the HR person will provide the website and if you are pleasant, can probably be talked into signing you up.
Even if yours is a complicated case, contacting HR and having theses discussions if good because apparently everything gets recorded and transcribed into your record - they will flag your desire for certain coverage and (in my experience) forward it to the group who will be handling that aspect (e.g., choice of medical plan) so you get plenty of communications.
1 - you call them, don't wait for the various communications that are supposed to be generated within 30 days, which may never show up and then you forget about them. Get all this straightened out. The only one who ultimately cares about you, is you.