My thoughts are to proceed w/caution no matter how you proceed. Objectively, the Seller can tell you to take a hike and, thus, take his chances on another potential 'victim' (or Buyer.) There are LOTs of folks out there that don't hire a Home Inspector.
Now, if you're really interested in the house, I think that his offer to pay for half is very generous. You see, he will benefit from the information that's learned whether you buy, or not. If you don't, he's all the wiser. The key here is how bad do you want the house??? If you want it REALLY bad, but will only make a decision on what the ENgineer says, then you should be willing to pay for the ENTIRE fee that the Engineer will charge. So, your decision here can 'hinge' on your emotions. (I don't know.)
You didn't ask but what I would do is, first, hire a Real Estate Attorney too. His job is to be SURE that whatever it is that gets WRITTEN (whether is contracts or Engineer costs), it's all written to protect YOUR interests! A Real Estate Attorney is VERY cheap right now. Later on, should you decide to sue, it will cost you a WHOLE lot more because you don't have one ALREADY retained.
After hiring the Attorney, you DON'T agree to ANYTHING until you talk to him/her. Got it??? What I would propose to you is you get the Seller to hold off on paying any fees at this time (so you need to ASSUME that, at worst, YOU will pay for everything because there's nothing in writing.) Consult your ATtorney to see if he (i.e., you) and the Seller can agree to hold off on having other potential Buyers look at the house until you have an Engineer inspect AND GIVE ESTIMATES on what it would take to PROPERLY fix the 'problem'. (Maybe you all agree to 5 days, then put it in writing, then sign it.) This way, once you have ALL the Engineering fees (which MAY run into MORE $$$ than just his fee), and all the ESTIMATD REPAIR COSTS, perhaps you can propose to the Seller to DEDUCT that cost, plus 10%, off of the SELLING PRICE. In doing it this way, (assuming the house needs to sell AND you're very, VERY interested in buying it but you don't really let him know how excited you are), it costs you nothing (at this time), AND you get the house for less $$$ up-front. (Whether you end up having the problem fixed or not is another matter.) OR, the 2 of you can 'split' the expense, OR you can ask the Seller to pay for ALL the fixes, OR you can hve $$$ put in escrow, OR whatever. You see, once you have ALL the costs in front of you, you and YOUR lawyer can make a NUMBER of proposals, starting with the one that benefits you the most.
Sorry for rambling on for so long. My best to ya and hope this helps.
Jay J -Moderator
PS: Hire that Attorney and DON'T sign or agreee to ANYTHING w/o talking to one ...
PPS: God Bless America!