#No, it can't.
No, it can't.
Nothing supports this.
Players' expectations of an item are in keeping with the knowledge available about said item. If a bag of holding is modified in such a way as to allow opening from the inside, it's something players should be aware of, specifically so they can guard against scenarios presented like the one you have illustrated above. To elaborate slightly, this isn't to say your players would know about every magical item in every way, but a bag of holding is fairly common and is something every adventurer gets their hands on as soon as possible.
For those asking about the source for this:
DMG Pg. 153-154 Bag of Holding
The description does not provide that the bag can be opened from the inside. The picture also provides visual cues that indicate the bag is latched shut in some fashion from the outside (this is likely due to prevent it from being accidentally filled with items that would exceed it's 500 lb weight limit and destroy it and your contents, for example if you were to fall into a river.)
As always in 5e, and since every answer seems to require this as a repeat: Rule Zero trumps everything.