The bug

In spectator mode you have the same block and entity reach distance as in survival or adventure mode when you try to open containers.
I would expect it to use the reach distance of creative mode as a higher reach distance gives no gameplay advantage in spectator mode but makes interaction a little bit easier.

How to reproduce

1. Change your gamemode to creative
2. Stand in the middle of a block
3. Use the following command or just place a chest in +x direction manually

   /setblock ~1 ~ ~ chest
   

4. Use the following command

   /tp ~-4.4 ~ ~
   

5. Try to open the chest; it should work
6. Switch to spectator mode and try to open the chest again
   → You are unable to open the chest

The reason

The following is based on a decompiled version of Minecraft 1.10 using MCP 9.30.

The method net.minecraft.client.multiplayer.PlayerControllerMP.getBlockReachDistance() returns only 4.5 if the player is in creative mode otherwise it returns 4. Additionally the method net.minecraft.client.multiplayer.PlayerControllerMP.extendedReach() is called to test if the player is in creative mode and in that case sets the entity reach distance to 6 (might not be the case anymore in 1.11+).