Not true. This isn't android. On android, the OS informs the apps that they should close. A poorly behaved app can ignore it.
On iOS, the OS invokes the app on each event and expects it to respond back. If it doesn't, it's assumed hung and killed immediately. iOS apps that run in background have to constantly ask for permission. If they don't respond they get killed at most within 10 minutes.
Correct.
On Android, apps can do whatever they want in the background, thus a buggy app can drain the battery, hog memory, crash the OS, etc.
On iOS, apps can only do limited things in the background: Play audible content, check for location, VoIP, receive updates from external accessories, or Newstand apps that download and process content.
Both are true multi-tasking, Android is a no-holds barred multi-tasking system, and iOS is a controlled multi-tasking system. Both have their positives and negatives.
It's like being a 17-year old, and going to a house party where there is no supervision, vs. the parents of the house supervising the party.
There is more of a chance for different 'questionable' activities going on at the unsupervised party, but there is also a chance that the house might be trashed or things stolen at that party.
For a supervised party, the house will most likely be fine after the party, none of the guests will get STDs or become pregnant, but it might not be as 'interesting or fun'.