Ordinarily, a landlord must give notice before entering a leased property. However, one exception to that rule is when the premises have been abandoned. RCW 59.18.150(5) provides that "The landlord may enter the dwelling unit without consent of the tenant in case of emergency or abandonment."
If the letter that you received from the tenant stated that the property had been vacated (as opposed to was going to be vacated), then you would appear to be well within your rights, at least to verify the abandonment.
In the alternative, the tenant gave you notice of a dangerous condition on the property. Under RCW 59.18.070, that required you to commence remedial action within either 24 or 72 hours. A tenant cannot reasonably give you notice of a problem at the property and then complain when you show up to fix it.
I suggest that you send the tenant's lawyer a copy of the tenant's letter along with the two RCW citations. Unless there is more to your story, that should answer the attorney's a concerns.
This is legal information and not legal advice. The final answer to your question will depend on more facts than you can include in your question and some that you probably would not think to include. Treat this as a starting point, not the answer.