You then have to ask: Where do the assessments come from? Assessments are meant to generally reflect the value of the home. So usually the county will look at price trends in a particular community or particular area, including recent purchases, and adjust values accordingly.
Sometimes, the county will "re-set" a property's assessment when it's sold. And that makes sense. Sometimes, over the years, the general adjustments a county does don't exactly reflect the true price changes. And little errors build up. That's why buyers and sellers are told never to use an assessment to determine value. It's just not accurate.
So, if your county resets a property's value after a sale, yours may well be adjusted--in your case, down to $250,000 to reflect the true value of the property. It should be fairly easy to find out your county's policy. Just ask. And, looking online, it appears that Alameda County will reassess when you buy. From its web site: "Under Proposition 13, real property is reappraised only when a change in ownership occurs, or after new construction is completed. Partially completed new construction is also added as of January 1. Generally, a change in ownership is a sale or transfer of property, while new construction is an addition or improvement to property. Except for these two instances, property assessments cannot be increased by more than 2% annually unless the Assessor has previously granted a temporary reduction due to market value decline." See http://www.acgov.org/assessor/assrinfo.htm#assess
Also from Alameda County's web site (same page): "Change in Ownership Reappraisals
When a transfer occurs, the Assessor receives a copy of the deed and determines if a reappraisal is required under State law. If it is required, an appraisal is made to determine the new market value of the property. The property owner is then notified of the new assessment and has the right to appeal the value. Interspousal transfers do not require a reappraisal."
So your assessment should drop to $250,000. However, you will want to stay on top of that and if a future tax bill continues to reflect a value of $300,000, you should protest it. Based on the county's web site, you should be able to get the assessed value down to $250,000.
Why did the title company use $300,000? Because that's the most recent assessment. That's what's being charged now. That's just the way it's done.
So: Keep an eye on what the county does. But, from what it says on its web site, your assessment should drop.
Hope that helps.
I heard Lots of states have begun to value property at the last sales price, in which case, the assessment would self correct, at your purchase price?