Ok, I believe I must have pressed save, otherwise those checkboxes would still be next to the other folders.
I went into your 2nd option & sure enough, only primary is checked off.
So a couple of things:
1. The reason I thought it didn't work, is b/c I didn't get an e-mail in TB that I was waiting for. I found it in the updates folder. I had to resend the e-mail & then I got it the 2nd time.
2. I just went back into those other folders which have HUGE numbers of e-mail in them & to the right of the sender it says "Inbox" all in grey. I assume that means it's telling me they all went to the inbox, so why are they still in those folders?
And why did that e-mail that triggered me that there was a problem, not come through to TB or I'm pretty sure, the inbox in gmail?
Thunderbird may have already downloaded that email (or its header, depending on Thunderbird's synchronization settings) and you just didn't see it. I don't think you understand how the Gmail inbox tabs work or what they are. They are not folders/labels into which your emails are put. They are just smart views applied to your inbox. All non-junk/non-spam emails that you receive are still stored in your inbox, whether you turn on the inbox tabs or not. The tabs do not affect where your emails are stored, they only affect how they are displayed in your inbox (in Gmail's web interface). Thunderbird or any other email client will download all those messages into one inbox, whether inbox tabs are turned on or not.
There is another feature of Gmail that's very similar to the inbox tabs and can be quite confusing if you don't differentiate them. They are called categories and they too are not folders into which your received emails are stored. They are just smart groups into which all your inbox messages are categorized for viewing purposes and not storage purposes. There is a category that matches each inbox tab (except for the primary tab), so these categories and inbox tabs work together such that each inbox tab displays the emails grouped in the corresponding category. For example, the Updates tab (if enabled) will display emails that are in the Updates category. If you disable inbox tabs (like you did), the categories are not affected and remain visible in the left panel of the Gmail web interface, so that you can still view messages in the individual categories even after inbox tabs are turned off. This is why you thought turning off the inbox tabs did not work. It worked alright, but the categories are still listed in the labels list on the left panel, unless you hide the categories so that they are not shown in the labels list.
Remember, the inbox tabs and their corresponding categories are not folders into which your emails are stored. The inbox tabs are simply views while the categories are simply groups into which your inbox emails are filtered, for viewing purposes. If you want all inbox messages displayed in one (primary) tab, you turn off the inbox tabs. If you want the categories to be hidden from the left panel, you hide them (Go to Settings -> Labels -> Categories, in the Show in label list column, choose hide next to each individual category or choose hide next to Categories to hide them all). Email clients do not care about the inbox tabs or categories, they'll download all inbox messages into one inbox.