It's important to be aware of two separate concepts: right to inspect, and as-is/disclosures.
The right to inspect should be specified, but it may also be implicit according to local laws - with such a large purchase as a house you should always get a professional, such as a real estate lawyer, to advise you on your local laws and regulations. Generally speaking, though, you should always always have the right to inspect and cancel the contract if anything is discovered in the inspection that turns off your personal interest in the property. You may or may not need to forfeit "earnest money", if you have any in the property, but this varies by jurisdiction and contract. Often you can walk-away with nothing more than time lost and your personal expense in getting a home inspection, but again you should confirm with a local professional.
The other issue is the implied condition of the property. When you sell a house you have a legal obligation to disclose issues you know it has - if the roof leaks or the furnace has gone out, it's illegal to not say so. A statement of "as-is" has the meaning that the seller disavows all personal knowledge of the property, and further they are saying "even if something is wrong with the property I'm not going to pay to fix it". In a normal sale condition if it turns out the roof is leaking the owner will fix it up as a condition of the sale, and thus the original offer price is still good.
Legally, in most jurisdictions if the seller still knows anything is wrong with the house they still have to say it, and stating as-is does not absolve them of this responsibility - but as-is is basically a statement of "other than what I've disclosed that I know is wrong - if anything - I'm telling you I don't otherwise know nor do I care about any further condition of the property". This situation is most common with banks and properties being sold by non-occupant relatives, who honestly don't know about the property themselves because they don't live there.
So as-is means it's on you to inspect the property and insure it's what you thought and want. But you know what? This is absolutely always the case, and I don't know why anything would think otherwise - you should never trust someone who is trying to sell an expensive item to you simply at your word, you must verify everything. To do otherwise is so naive as to be intolerably foolish - trust nothing, verify everything. A fool and his money are soon parted!
In conclusion, please do verify your local laws and regulations support your right to inspect (at your own cost), and then you can go ahead and accept the offer with a clear mind - and buy yourself a good, thorough home inspection! If everything checks out then you can proceed to sale, and otherwise you can cancel the contract and move on or re-start negotiations.