I would still call that indigestion, nobody would call it food poisoning, other than you it looks like.
Also, having vomited more than once in my life, it would definite improvement, indeed probably a considerable improvement, if it tasted and smelled like branston pickle... unless that smell became associated with vomit and people reacted accordingly which would be bad as that would probably deprive me of a fine class of sandwich filling. This applies to booze fuelled and other kinds.
On American pickles owing to many people maintaining a stock of a variety of brands I have tried many many different brands, sometimes without thinking when I am there ordering a burger -- it was almost as much of a culture shock as people not drinking squash and sales tax not being included in the price on the shelf. The only thing I found more disappointing was either ordering a burger with chillies when I was going through chilli withdrawal and it coming with 4 jalapeños (that I can write off as a one off/fault of the restaurant I was in) or ordering with onions as an extra on my burger and getting some fine chopped raw onion rather than shallow fried onion that had been sliced into rings. I will grant that some American pickes were vaguely tolerable, given pickles elsewhere are actually nice most of the time we get to use terms like abomination.
What I find is in US pickling, as you say, things are put in brine which is OK for some things*, what most of the rest of the world calls pickling typically involves putting things in various types of vinegar with a few spices (in Europe this is usually Coriander seeds) -- I could quite happily a glass of the juice at the end of pickling as I know it, and sometimes have a little splash when getting one out of the jar**, but even I am inclined to wretch at the prospect of doing it for US pickle juice. The straight brine thing would put it in the realms of fermentation elsewhere, though strictly speaking picking in vinegar is a type of fermentation, and brine is an option for some things.
Depending upon the age of the person you are speaking to you can pickle basically any solid food and I would probably agree. That is not to say I am a fan of all of it -- pickled eggs I can leave and for pickled onions I prefer the small (silverskins) over the larger options, though I would not bother with any pickled onions beyond monster munch if given the chance. Pickled cabbage varies though it is usually someone's grandma that makes the best stuff and pickled fish depends upon the fish. Beetroot is nasty in all its forms as far as I am concerned. Anyway this is calling you out on your poor definition of food poisoning and not a GBAchef article so I will leave it there bar the footnotes.
*it is done elsewhere, however in those cases it is typically a storage method rather than a method that attempts to effect a taste change.
**in my experience it is a popular pregnancy food craving.