I've met foreigners who have had TERRIBLE tones but still manage to get their point across in Mandarin because of context. Your explanation for why English works despite mispronunciation is the same reason why Chinese works: context. For example, let's assume we were talking about our families. You want to say: 我爱我妈 (wo ai wo ma) "I love my mother". But if you said 我爱我马 (wo ai wo ma) "I love my horse", I would assume you meant you love your mother because of the context.