This immediately reminded me, first off, of an excerpt for Dave Yewdall's book about the "Big Sound" (or Hollywood Sound):
The "Big Sound"
The key phrase being "It's a philosophy, an art - an understanding of what sounds good together to make a bigger sound."
The 'Hollywood sound' is a gestalt, or culmination, of individual parts and pieces fitting together in dynamic and complimentary ways which exude big, bold, and ballsy attitude (when such attitude is called for) - while at the same time having the composure within this gestalt to introduce rich subtleties and tasteful depth of contrast. What I'm getting at here is that the Hollywood sounds can't be bought outright, yet they ARE something that you are capable of creating yourself - it comes down to having the right source elements to work with, and the experience and wisdom gained over time of how to dramatically piece these puzzle pieces together in ways which effectively work to achieve that Hollywood sound (and do so quickly/efficiently). It's a slight digression from the topic question, yet I feel it's an important foundation to begin to address your question since the word "Hollywood sound" is being thrown around incorrectly as a noun in my opinion, when actually it's more a verb.
The question you pose then seems to be directly at it's core an ethical issue regarding your tangible source sound elements, or assets. Source elements can be bought legally from a variety of providers, some which have studio ties - for example, The Hollywood Edge is a distribution division of CSS Studios, which owns Soundelux/Todd-AO, and nearly everything from The Hollywood Edge label is in same way, shape, or form sound source that comes straight from the vaults of Soundelux itself. These are top, proven-to-work Hollywood sounds But even so, these sounds aren't "The Hollywood sound" itself in their own right - nice recordings, yes, but it still matters how you piece them together dynamically and dramatically. Many times this "Hollywood sound" is developed using a composite of bought source material from known libraries, along with custom sound effects recordings of our own. But who cares what we use as long as we create a believable sound? In the end, if "it sounds good, is good".
To come full-circle to your primary question, my personal thought on the situation you pose is that you are taking the correct ethical approach of choosing to work with material you are allowed to use (or record yourself). I strongly commend you for that. But "sound effects source" from copyright FX libraries are perfectly okay too as long as you purchased a license to the library - and trust me, we all use these libraries to pull from, even ones we feel dirty for using sometimes cough cough General 6000 cough cough ;)
And even more, please embrace your recording and editorial skills regardless of what anyone else says. We all have the power and the ability to create the 'Hollywood sound' with our recordings. Your own effects CAN be as good as the major effects, it is indeed attainable. The catch is most of these 'Hollywood sound' type effects are layered and processed in such a way that, yes, a raw single-layer recording of a punch may not be encouraging. But take a meat slap, a bone crunch foley sound, and other such 'foley-able' sounds and edit them together, slam it with a compressor and you can begin to turn these possibly discouraging recordings into a big Hollywood-style punch that is rounded out with a nice thud which hits you in the chest, an ear-piercing crack, and frieghtening flesh slap.
The bigger, primary part of question regarding him/her determining what you use is: it's not their business to tell you what to do. Especially so because it is not paid work. But even so, it's not their business to tell you what to use, and furthermore, undermine you by saying in effect "your sounds can't meet the cinema standard". For example, a client will provide suggestions for what they want their combat aesthetic to sound like (sock punches versus realistic versus cinematic sensational versus hyper-real), but it's not their place to judge what source I'm going to use to develop that sound (and in most cases I know what my go-to's are for each style) - it's not their area of expertise quite frankly to dictate what source I use, and by them approaching me (or you), it's because they value (or should value) the sound judgements you can make about what the right source material is required for developing the aesthetic they want to achieve, in this case, to achieve the "Hollywood sound'. The journey now is developing your creations to mirror a similar aesthetic with your own signature on it. You used your own recordings? so what! If they combine (on their own or in tandem with bough library FX) to achieve the end result of the 'Hollywood' aesthetic, who gives a damn that it was your own material ;)
Good luck with 'wrangling' the client on this one! Sometimes these types of clients can be the trickiest to handle, yet so far it appears that you're doing so with grace and a strong sense of ethical well-being and professional integrity (which is the right road). Embrace it! The silver lining in this situation: this gives you a fantastic opportunity to study the 'Hollywood sound' of others and work at achieving the same type of aesthetic from the ground-up the SAME WAY all these big shows' 'Hollywood sound' started from -> the raw source recordings! The world is your oyster in this situation if you choose to look at it from the angle of "lets create this Hollywood sound he wants to hear".
Hopefully that wasn't too long-winded Melissa. It's such a multi-faceted question!