Your person in question is right: You can cast emergency force sphere while in the midst of casting summon monster.
First, there's nothing in the text of emergency force sphere that explicitly forbids it.
There's also nothing in the text describing actions that forbids the use of an immediate action during another action. According to the description of immediate actions, "an immediate action can be performed at any time — even if it's not your turn," and "You cannot use another immediate action or a swift action until after your next turn if you have used an immediate action when it is not currently your turn... You also cannot use an immediate action if you are flat-footed." That seems to be the entire extent of the rules governing when immediate actions cannot be used. There's no prohibition there against using immediate actions while casting another spell.
Immediate actions are based on swift actions; The text describing those explicitly mentions that swift actions can be used to cast spells, and there's nothing there about that being impossible when you're already casting a different spell. There's also the line "You can take a swift action anytime you would normally be allowed to take a free action."
It sounds like the section on free actions us the next place we should look... And it seems there's nothing prohibiting those during another action, either. In fact, looking at the description of Action Types, there's even this line: "You can perform one or more free actions while taking another action normally." So there's explicit rule support for taking a free action while taking another action - and therefore support for taking a swift or immediate action in the same circumstances.
You did mention that concentration is necessary for spellcasting, and you're right about that; It's mentioned here that "If you start casting a spell but something interferes with your concentration, you must make a concentration check or lose the spell." However, the list of circumstances that force you to make concentration checks does not include "casting a spell" - in fact, there's nothing even comparable in the table.
In the absence of any evidence that casting a spell as an immediate action interferes with any other spell you might happen to be casting at the same time, I have to say that the RAW supports your friend.
Oh, and you describe Pathfinder as being a "rules-can" game, meaning that it only lets you do something if that something is explicitly permitted by the rules. You are wrong about this. Things the rules do not expressly permit include writing mundane text using writing materials from the equipment lists, donning and doffing non-armour clothing, and overloading a rowboat until it sinks. All of these things, and more, are permitted. The Pathfinder is neither a rules-can game nor a rules-can't game; Like most role-playing games, it's "rules-incomplete."