This isn't about trust. The scenario could have played out like this, if one branch didn't broadcast their block:
AntPool finds block outside of China. The block propagates fine for the rest of the world, but has issues getting through the GFW. While it's trying to get to China, ViaBTC in China finds a block. Since they have not gotten the AntPool block yet, they propagate their block. ViaBTC manages to propagate throughout all of China, while AntPool propagates everywhere else. If the next block is found by a Chinese miner who built on ViaBTC's block, AntPool's block would have been orphaned, even if it was technically mined earlier.
I believe this happened in the past with KanoPool & BTC.com. KanoPool found a block a few seconds before BTC.com, but BTC.com (located in China) also broadcasted their block. The next block was found by BTC.com, so Kano's block was orphaned.
Once a miner finds a block it starts relaying it to its peers, for each peer to be convinced about the authenticity of the block, both the lucky miner and the peer should go through a rather lengthy protocol in which the bottleneck is not the communication channel but the ability of the peer to validate it mainly by comparing each of the transactions included in the block against the UTXO (blockchain state) besides a lot of other measures, like running the input scripts, checking consensus rules, ...
Unless the peer finds everything consistent, it doesn't care about the block under consideration and specifically it won't interrupt its own mining operations (if any) and it won't start relaying the block (at least before passing some specific steps).
But when it is about the branches of a same pool, the situation is radically different:
They can switch to new job start relaying it almost immediately, simply because they are not peers!
They are multiple instances of a single entity and trust each other.
If Antpool is so naive that runs each of its branches just like an independent pool, it doesn't deserve its reputation for being big and attractive and if it has adjusted its intra-p2p protocol to avoid such a meaningless and time consuming "re-validation", how is it possible for it to relay two blocks simultaneously and competitively, without a bad intention?
As of Kano/btc.com case it is obviously a competition between two blocks of two different miners and normally happens with orphan blocks as its result.