Our current environment is SharePoint standard edition. As per the research done, I find that to open infoPath in browser requires SharePoint Enterprise edition. Is this true? or is there any possibility to open form in browser to fill out.
Is this true?
Yes, it's correct, the Infopath service is only available with SharePoint Enterprise Edition, and can't be used in Standard edition. you can also check the Feature Comparison between Standard and Enterprise.
Is there any possibility to open it form in browser to fill out?
What should you do?
Use default forms, or develop your forms in the visual web part or use other 3rd tools like formotus.
Start the SharePoint 2013 Management Shell.For Windows Server 2008 R2:
On the Start menu, click All Programs, click Microsoft SharePoint 2013 Products, and then click SharePoint 2013 Management Shell.
On the Start screen, click SharePoint 2013 Management Shell.
If SharePoint 2013 Management Shell is not on the Start screen:
Right-click Computer, click All apps, and then click SharePoint 2013 Management Shell.
Run the below command
Set-SPInfoPathFormsService -AllowUserFormBrowserRendering $true