During a tune up I don't know if they would or not, but you'd thought they'd check the elctrical also ( which would then lead to Battery and alternator).. but never went to a shop for a tune up.
I"ve never seen a battery do that unless it was shorted for a period of time.. most battery that dies.. well.. dies.. they no longer hold charge.. thats it thats all.. and if it was gettin that bad, you'd think you'd see your terminal start turning green from the acid before it actually falls off like that.. but again.. I don't have my knowledge about tune ups and battery issue ( other then stripped terminal and bad connection )
If you have lost confidence, my advise is not to go.. YOU yourself is the only person that will lie to yourself LAST ( unless you're a ricer and being watchin too much fast and furious
but that'* another case ).
I'm going to Email the Ontario Chapter Bonneville Club bout this post and hopefully someone can recommend a good shop thats not too far for you ( my shop would be good 2 hours away of a drive for you )
P.*. If you'd like to be added to the Ontario BonnevilleClub mailin list.. please PM me your email addy and I will add it in.