Well, not ANYthing. Wood can be even too crappy for a laminated bow, but you can get away with a little more grain and/or ring runout, or use flat sawn lams that aren't the greatest, but in my experience, sub-par wood often makes sub-par bows in spite of our best efforts regardless of the constuction/design and can be harder to work with tools, harder to tiller properly, less durable, etc. IMO, we should strive to use the best wood we can get our hands on.
I used to use only the best wood for selfbows and set aside the second rate stuff for bamboo backed bows and such, but not anymore. I had problems getting a good tiller on a few of them due to the ring runout so I started using only the best wood for backed bows too and my bows are better for it.