Yes, non-resident aliens and foreign companies can file for US trademark registration but must disignate a "domestic representative" to communicate with the US Patent & Trademark Office. A prudent thing would be an agreement between your two companies. No one on Avvo can or will give you a trademark clearance without being retained.
The above is general legal and business analysis. It is not "legal advice" but analysis, and different lawyers may analyse this matter differently, especially if there are additional facts not reflected in the question. I am not your attorney until retained by a written retainer agreement signed by both of us. I am only licensed in California. See also avvo.com terms and conditions item 9, incorporated as if it was reprinted here.
While the other similarly named website is not registered with the PTO, this does not mean that it is not entitled to trademark protection. Common law trademark rights arise from the actual use of a mark and afford limited rights to the trademark ownership (among others, there is a geographic restriction to common law trademark protection, but this may not apply here if the website is being accessed globally).
So, as my colleague suggests, you should try and reach out to them and get their consent in writing if you'd like to enter the industry without exposing yourself to liability. You should not hand your competitors a good tool of getting rid of you or of hurting you financially. This is just scratching the surface of potential problems with your project, it would be a good idea to retain legal representation to get this sorted.