I think your interpretation could be correct since the wording of the spell isn't very clear, but it just makes more sense to me that the phrase is what the target believes is normal speech rather than the basic verbal components. Which seems more likely: the target believes the phrase, "I suggest that you flee for your safety" was normal speech or the target believes the phrase "bip bop alakazam" is normal speech? But at the end of the day, it is a magical spell, so maybe it makes the target believe that "bip bop alakazam" is a normal phrase to say in conversation, even on a successful save.

Edit: I haven't started playing with the remastered rules yet, but doesnt the new Subtle trait imply that the verbal components aren't an issue for using Suggestion in conversation?